If ∫ f ( x ) d x = ψ ( x ) , then ∫ x 5 f ( x 3 ) d x , is equal to

1 3 x 3 ψ ( x 3 ) − ∫ x 2 ψ ( x 3 ) d x + c

1 3 [ x 3 ψ ( x 3 ) − ∫ x 3 ψ ( x 3 ) d x ] + c

1 3 [ x 3 ψ ( x 3 ) − ∫ x 2 ψ ( x 3 ) d x ] + c

1 3 x 3 ψ ( x 3 ) − 3 ∫ x 3 ψ ( x 3 ) d x + c

MEDIUM

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If $\int \frac{1 - 2019 \cos^{2} x}{(\sin x)^{2019} \cos^{2} x} d x = \tan x \cdot f (x) + C$ where $' C'$ is an integral constant then $f (\frac{π}{2}) + f^{'} (\frac{π}{2}) + f (- \frac{π}{2})$ is equal to

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Important Questions on Indefinite Integration

HARD

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

The value of

\int \frac{2 x + \sin 2 x}{1 + \cos 2 x} d x

is equal to

HARD

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

The integral

\int \frac{d x}{{(x + 4)}^{\frac{8}{7}} {(x - 3)}^{\frac{6}{7}}}

is equal to: (where

C

is a constant of integration)

MEDIUM

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

\int x^{3} \sin 3 x d x =

MEDIUM

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

The integral

\int {(\frac{x}{x \sin x + \cos x})}^{2} d x

is equal to, (where

C

is a constant of integration):

EASY

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

The integral

\int c o s (lnx) d x

, is equal to

MEDIUM

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

\int \frac{x^{9}}{{(4 x^{2} + 1)}^{6}} d x

is equal to

MEDIUM

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

\int \frac{\cos x d x}{\sin^{3} x {(1 + \sin^{6} x)}^{\frac{2}{3}}} = f (x) {(1 + \sin^{6} x)}^{\frac{1}{λ}} + c

, where

c

is a constant of integration, then

λ f (\frac{π}{3})

is equal to

MEDIUM

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

The integral

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

is equal to

EASY

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

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

is equal to: (where

C

is an arbitarary constant)

HARD

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

The integral

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

, is equal to

HARD

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

\int \sin^{- 1} (\frac{\sqrt{x}}{1 + x}) d x = A (x) \tan^{- 1} (\sqrt{x}) + B (x) + C

, where

C

is a constant of integration, then the ordered pair

(A (x), B (x))

can be

HARD

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

\int x^{5} e^{- 4 x^{3}} d x = \frac{1}{48} e^{- 4 x^{3}} f (x) + C

, where

C

is a constant of integration, then

f (x)

is equal to

MEDIUM

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

\int \frac{\cos 2 x - \cos 2 α}{\cos x - \cos α} d x =

EASY

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

\int e^{x} secx (1 + tanx) dx =

MEDIUM

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

\int e^{2 x} (\cos x + 7 \sin x) d x = e^{2 x} g (x) + c

, where

c

is a constant of integration, then

g (0) + g (\frac{π}{2})

is equal to______.

MEDIUM

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

If $I_{n} = \int x^{n} \sin x d x$ and $I_{6} - 360 I_{2} = f (x) \cos x + g (x) \sin x,$ then $f (1) + g (1) =$

MEDIUM

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

$\int \frac{\tan^{- 1} x}{x^{3}} d x =$

HARD

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

\int x^{5} e^{- x^{2}} d x = g (x) e^{- x^{2}} + c

, where

c

is a constant of integration, then

g (- 1)

is equal to

HARD

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

The value of the integral

\int \frac{e^{x} (x^{2} + 1)}{{(x + 1)}^{2}} d x =

MEDIUM

Mathematics>Integral Calculus>Indefinite Integration>Methods of Integration

\int f (x) d x = ψ (x)

, then

\int x^{5} f (x^{3}) d x

, is equal to

If ∫1-2019cos2x(sinx)2019cos2xdx=tanx·f(x)+C where 'C' is an integral constant then fπ2+f'π2+f-π2 is equal to

Important Questions on Indefinite Integration

Learn and Prepare for any exam you want !

If $\int \frac{1 - 2019 \cos^{2} x}{(\sin x)^{2019} \cos^{2} x} d x = \tan x \cdot f (x) + C$ where $' C'$ is an integral constant then $f (\frac{π}{2}) + f^{'} (\frac{π}{2}) + f (- \frac{π}{2})$ is equal to