Indefinite Integration Questions

MathematicsIndefinite Integration30 Questions Found

MathematicsEvaluation of Special Integral FormsJEE Main 2004Moderate

$\int \frac{d x}{c o s x - s i n x}$ is equal to

(A)

\frac{1}{2} lo g tan (\frac{x}{2} + \frac{3 π}{8}) + C

(B)

\frac{1}{2} lo g cot (\frac{x}{2}) + C

(C)

\frac{1}{2} lo g tan (\frac{x}{2} - \frac{3 π}{8}) + C

(D)

\frac{1}{2} lo g tan (\frac{x}{2} - \frac{π}{8}) + C

Answer:A

MathematicsFundamental Integration FormulasJEE Main 2004Easy

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If $\int \frac{s i n x}{s i n ( x - α )} d x = A x + B lo g sin (x - α) + C$ , then value of $(A, B)$ is

(A)

(- cos α, sin α)

(B)

(cos α, sin α)

(C)

(- sin α, cos α)

(D)

(sin α, cos α)

Answer:B

MathematicsEvaluation of Special Integral FormsJEE Main 2005Easy

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$\int {\frac{l o g x - 1}{1 + ( l o g x ) ^{2}}}^{2} d x$ is equal to

(A)

\frac{l o g x}{( l o g x ) ^{2} + 1} + C

(B)

\frac{x}{x ^{2} + 1} + C

(C)

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

(D)

\frac{x}{( l o g x ) ^{2} + 1} + C

Answer:D

MathematicsIntegration by SubstitutionJEE Main 2007Easy

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$\int \frac{d x}{c o s x + 3 s i n x}$ equals

(A)

lo g tan (\frac{x}{2} + \frac{π}{12}) + C

(B)

lo g tan (\frac{x}{2} - \frac{π}{12}) + C

(C)

\frac{1}{2} lo g tan (\frac{x}{2} + \frac{π}{12}) + C

(D)

\frac{1}{2} lo g tan (\frac{x}{2} - \frac{π}{12}) + C

Answer:C

MathematicsIntegration by SubstitutionJEE Main 2008Easy

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The value of $2 \int \frac{s i n x d x}{s i n ( x - \frac{π}{4} )}$ is

(A)

x + lo g cos (x - \frac{π}{4}) + c

(B)

x - lo g sin (x - \frac{π}{4}) + c

(C)

x + lo g sin (x - \frac{π}{4}) + c

(D)

x - lo g cos (x - \frac{π}{4}) + c

Answer:C

MathematicsEvaluation of Special Integral FormsJEE Main 2012Easy

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If $\int \frac{5 t a n x}{t a n x - 2} d x = x + a ln ∣ sin x - 2 cos x ∣ + k$ , then $a$ is equal to

(A)

- 1

(B)

- 2

(C)

1

(D)

2

Answer:D

MathematicsIntegration by PartsJEE Main 2013Moderate

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If $\int f (x) d x = ψ (x)$ , then $\int x^{5} f (x^{3}) d x$ is equal to

(A)

\frac{1}{3} [x^{3} ψ (x^{3}) - \int x^{2} ψ (x^{3}) d x] + C

(B)

\frac{1}{3} x^{3} ψ (x^{3}) - 3 \int x^{3} ψ (x^{3}) d x + C

(C)

\frac{1}{3} x^{3} ψ (x^{3}) - \int x^{2} ψ (x^{3}) d x + C

(D)

\frac{1}{3} [x^{3} ψ (x^{3}) - \int x^{3} ψ (x^{3}) d x] + C

Answer:C

MathematicsIntegration by PartsJEE Main 2014Moderate

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The integral $\int (1 + x - \frac{1}{x}) e^{x + 1/ x} d x$ is equal to

(A)

(x + 1) e^{x + 1/ x} + c

(B)

- x e^{x + 1/ x} + c

(C)

(x - 1) e^{x + 1/ x} + c

(D)

x e^{x + 1/ x} + c

Answer:D

MathematicsIntegration by SubstitutionJEE Main 2015Easy

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The integral $\int \frac{d x}{x ^{2} ( x ^{4} + 1 ) ^{3/4}}$ equals

(A)

- (x^{4} + 1)^{1/4} + c

(B)

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

(C)

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

(D)

(x^{4} + 1)^{1/4} + c

Answer:B

MathematicsIntegration by SubstitutionJEE Main 2016Moderate

View in:English Hindi

The integral $\int \frac{2 x ^{12} + 5 x ^{9}}{( x ^{5} + x ^{3} + 1 ) ^{3}} d x$ is equal to

(A)

\frac{x ^{5}}{2 ( x ^{5} + x ^{3} + 1 ) ^{2}} + C

(B)

\frac{- x ^{10}}{2 ( x ^{5} + x ^{3} + 1 ) ^{2}} + C

(C)

\frac{- x ^{5}}{( x ^{5} + x ^{3} + 1 ) ^{2}} + C

(D)

\frac{x ^{10}}{2 ( x ^{5} + x ^{3} + 1 ) ^{2}} + C

Answer:D

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$\int \frac{d x}{c o s x - s i n x}$ is equal to

If $\int \frac{s i n x}{s i n ( x - α )} d x = A x + B lo g sin (x - α) + C$ , then value of $(A, B)$ is

$\int {\frac{l o g x - 1}{1 + ( l o g x ) ^{2}}}^{2} d x$ is equal to

$\int \frac{d x}{c o s x + 3 s i n x}$ equals

The value of $2 \int \frac{s i n x d x}{s i n ( x - \frac{π}{4} )}$ is

If $\int \frac{5 t a n x}{t a n x - 2} d x = x + a ln ∣ sin x - 2 cos x ∣ + k$ , then $a$ is equal to

If $\int f (x) d x = ψ (x)$ , then $\int x^{5} f (x^{3}) d x$ is equal to

The integral $\int (1 + x - \frac{1}{x}) e^{x + 1/ x} d x$ is equal to

The integral $\int \frac{d x}{x ^{2} ( x ^{4} + 1 ) ^{3/4}}$ equals

The integral $\int \frac{2 x ^{12} + 5 x ^{9}}{( x ^{5} + x ^{3} + 1 ) ^{3}} d x$ is equal to

$\int \frac{d x}{c o s x - s i n x}$ is equal to

If $\int \frac{s i n x}{s i n ( x - α )} d x = A x + B lo g sin (x - α) + C$ , then value of $(A, B)$ is

$\int {\frac{l o g x - 1}{1 + ( l o g x ) ^{2}}}^{2} d x$ is equal to

$\int \frac{d x}{c o s x + 3 s i n x}$ equals

The value of $2 \int \frac{s i n x d x}{s i n ( x - \frac{π}{4} )}$ is

If $\int \frac{5 t a n x}{t a n x - 2} d x = x + a ln ∣ sin x - 2 cos x ∣ + k$ , then $a$ is equal to

If $\int f (x) d x = ψ (x)$ , then $\int x^{5} f (x^{3}) d x$ is equal to

The integral $\int (1 + x - \frac{1}{x}) e^{x + 1/ x} d x$ is equal to

The integral $\int \frac{d x}{x ^{2} ( x ^{4} + 1 ) ^{3/4}}$ equals

The integral $\int \frac{2 x ^{12} + 5 x ^{9}}{( x ^{5} + x ^{3} + 1 ) ^{3}} d x$ is equal to