If $\int f(x) d x=F(x)$, then $\int x^3 f\left(x^2\right) d x$ is equal to

$\frac{1}{2}\left[x^2\{F(x)\}^2-\int\{F(x)\}^2 d x\right]$

$\frac{1}{2}\left[x^2 F(x)-\frac{1}{2} \int\{F(x)\}^2 d x\right]$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int f(x) d x=F(x)

, then

\int x^3 f\left(x^2\right) d x

is equal to

View answer and explanation

Correct option: B

\frac{1}{2}\left[x^2 F\left(x^2\right)-\int F\left(x^2\right) d\left(x^2\right)\right]

Option B (

\frac{1}{2}[x^2 F(x^2)-\int F(x^2) d(x^2)]

) is correct because it is the result of applying integration by parts to the integral

\int x^3 f(x^2) dx

with a suitable substitution.