Question

x^3 tan^-1x integrat

Answer 1

∫x3tan-1(x)dx

Use integration by parts.

Let       u = tan-1x                      dv = x3dx

        du = 1 / (1 + x2)dx             v = (1/4)x4

Then the integral is

(1/4)x4tan-1x - (1/4)∫[x4 / (1 + x2)]dx

Then, you take the integral of the sub-integral.

∫x4 / (1 + x2)dx

Divide the polynomials

We get x^2 + 1/1+x^2 -1

integrating with respect to x

I = x^3/3 + tan^-1(x) -x

Hope it heps you!