Given the integral of f, find the integral of x^3 f(x^2) (or x^5 f(x^3)) by parts

1. A.
   $\frac{1}{3}x^3\psi(x^3) - 3\int x^3\psi(x^3)\,dx + c$
2. B.
   $\frac{1}{3}x^3\psi(x^3) - \int x^3\psi(x^3)\,dx + c$
3. C.
   $\frac{1}{3}x^3\psi(x^3) - \int x^2\psi(x^3)\,dx + c$
4. D.
   $\frac{1}{3}x^3\psi(x^3) - \int x^2\psi(x^3)\,dx + c$

Tap an option to check your answer.

1. A.
   $\dfrac{1}{2}\left[x^2 g(x^2) - \displaystyle\int g(x^2)\,d(x^2)\right]$
2. B.
   $\dfrac{1}{2}\left[x^2[f(x)]^2 - \displaystyle\int[g(x)]^2\,dx\right]$
3. C.
   $\dfrac{1}{2}\left[x^2 g(x) - \displaystyle\int g(x)\,d(x)\right]$
4. D.
   $\dfrac{1}{2}\left[x^2 g(x^2) + \displaystyle\int g(x^2)\,d(x^2)\right]$

Tap an option to check your answer.