Indefinite Integration Questions

MathematicsIndefinite Integration30 Questions Found

MathematicsEvaluation of Special Integral FormsJEE Advanced 1978

Evaluate $\int \frac{s i n x}{s i n x - c o s x} d x$

Answer:

\frac{1}{2} lo g ∣ sin x - cos x ∣ + \frac{x}{2} + C

MathematicsIntegration by SubstitutionJEE Advanced 1979

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Evaluate $\int \frac{x ^{2} d x}{( a + b x ) ^{2}}$

Answer:

\frac{1}{b ^{3}} [a + b x - 2 a lo g ∣ a + b x ∣ - \frac{a ^{2}}{a + b x}] + C

MathematicsIntegration by PartsJEE Advanced 1981

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Evaluate $\int (e^{l o g x} + sin x) cos x d x$

Answer:

x sin x + cos x - \frac{1}{4} cos 2 x + C

MathematicsEvaluation of Special Integral FormsJEE Advanced 1983

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Evaluate $\int \frac{( x - 1 ) e ^{x}}{( x + 1 ) ^{3}} d x$

Answer:

\frac{e ^{x}}{( x + 1 ) ^{2}} + C

MathematicsIntegration by SubstitutionJEE Advanced 1984

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Evaluate the following $\int \frac{d x}{x ^{2} ( x ^{4} + 1 ) ^{3/4}}$

Answer:

- (1 + \frac{1}{x ^{4}})^{1/4} + C

MathematicsIntegration by SubstitutionJEE Advanced 1985

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Evaluate the following $\int \frac{1 - x}{1 + x} d x$

Answer:

- 2 1 - x + cos^{- 1} x + x 1 - x + C

MathematicsIntegration by SubstitutionJEE Advanced 1987

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Evaluate $\int \frac{( c o s 2 x ) ^{1/2}}{s i n x} d x$

Answer:

\frac{1}{2} lo g \frac{2 + 1 - t a n ^{2} x}{2 - 1 - t a n ^{2} x} - lo g (cot x + cot^{2} x - 1) + C

MathematicsIntegration by SubstitutionJEE Advanced 1989

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Evaluate $\int (tan x + cot x) d x$

Answer:

2 tan^{- 1} (\frac{t a n x - c o t x}{2}) + c

MathematicsIntegration by SubstitutionJEE Advanced 1992

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Find the indefinite integral $\int (\frac{1}{3 x + 4 x} + \frac{l n ( 1 + 6 x )}{3 x + x}) d x$

Answer:

\frac{3}{2} x^{2/3} - \frac{12}{7} x^{7/12} + 2 x^{1/2} - \frac{12}{5} x^{5/12} + 3 x^{1/3} - 4 x^{1/4} + 6 x^{1/6} - 12 x^{1/12} + 12 lo g ∣ x^{1/12} + 1∣ + 6 {\frac{( 1 + x ^{1/6} ) ^{3}}{3} - (1 + x^{1/6})^{2} + 3 (1 + x^{1/6})} ln (1 + x^{1/6}) - {\frac{( 1 + x ^{1/6} ) ^{3}}{9} - \frac{3}{4} (1 + x^{1/6})^{2} + 3 (1 + x^{1/6})} + \frac{( l n ( 1 + x ^{1/6} ) ) ^{2}}{2} + C

MathematicsIntegration by PartsJEE Advanced 1994

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Find the indefinite integral $\int cos 2 θ ln (\frac{c o s θ + s i n θ}{c o s θ - s i n θ}) d θ$

Answer:

\frac{s i n 2 θ}{2} ln (\frac{c o s θ + s i n θ}{c o s θ - s i n θ}) - \frac{1}{2} ln sec 2 θ + C

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate ∫sinx−cosxsinx​dx

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate ∫(a+bx)2x2dx​

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate ∫(elogx+sinx)cosxdx

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate ∫(x+1)3(x−1)ex​dx

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate the following ∫x2(x4+1)3/4dx​

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate the following ∫1+x​1−x​​​dx

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate ∫sinx(cos2x)1/2​dx

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate ∫(tanx​+cotx​)dx

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Find the indefinite integral ∫(3x​+4x​1​+3x​+x​ln(1+6x​)​)dx

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Find the indefinite integral ∫cos2θln(cosθ−sinθcosθ+sinθ​)dθ

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate ∫sinx−cosxsinx​dx

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate ∫(a+bx)2x2dx​

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate ∫(elogx+sinx)cosxdx

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate ∫(x+1)3(x−1)ex​dx

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate the following ∫x2(x4+1)3/4dx​

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate the following ∫1+x​1−x​​​dx

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate ∫sinx(cos2x)1/2​dx

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Evaluate ∫(tanx​+cotx​)dx

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Find the indefinite integral ∫(3x​+4x​1​+3x​+x​ln(1+6x​)​)dx

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Find the indefinite integral ∫cos2θln(cosθ−sinθcosθ+sinθ​)dθ

Evaluate $\int \frac{s i n x}{s i n x - c o s x} d x$

Evaluate $\int \frac{x ^{2} d x}{( a + b x ) ^{2}}$

Evaluate $\int (e^{l o g x} + sin x) cos x d x$

Evaluate $\int \frac{( x - 1 ) e ^{x}}{( x + 1 ) ^{3}} d x$

Evaluate the following $\int \frac{d x}{x ^{2} ( x ^{4} + 1 ) ^{3/4}}$

Evaluate the following $\int \frac{1 - x}{1 + x} d x$

Evaluate $\int \frac{( c o s 2 x ) ^{1/2}}{s i n x} d x$

Evaluate $\int (tan x + cot x) d x$

Find the indefinite integral $\int (\frac{1}{3 x + 4 x} + \frac{l n ( 1 + 6 x )}{3 x + x}) d x$

Find the indefinite integral $\int cos 2 θ ln (\frac{c o s θ + s i n θ}{c o s θ - s i n θ}) d θ$

Evaluate $\int \frac{s i n x}{s i n x - c o s x} d x$

Evaluate $\int \frac{x ^{2} d x}{( a + b x ) ^{2}}$

Evaluate $\int (e^{l o g x} + sin x) cos x d x$

Evaluate $\int \frac{( x - 1 ) e ^{x}}{( x + 1 ) ^{3}} d x$

Evaluate the following $\int \frac{d x}{x ^{2} ( x ^{4} + 1 ) ^{3/4}}$

Evaluate the following $\int \frac{1 - x}{1 + x} d x$

Evaluate $\int \frac{( c o s 2 x ) ^{1/2}}{s i n x} d x$

Evaluate $\int (tan x + cot x) d x$

Find the indefinite integral $\int (\frac{1}{3 x + 4 x} + \frac{l n ( 1 + 6 x )}{3 x + x}) d x$

Find the indefinite integral $\int cos 2 θ ln (\frac{c o s θ + s i n θ}{c o s θ - s i n θ}) d θ$