Then under the indefinite integral radical (1+x 3) * dx 3 * 1/3).

Then (1+x 3) * d (x 3+ 1) is under the indefinite integer radical number 65438+3 *.

Let x 3 = y be (y+ 1/3) * d (y+ 1) under the indefinite integral radical.

The answer is 2/9 * y 3/2y = x 3.

Then 2/9 * x 2/9.

3) Let the radical sign (x+ 1)=t then x = t 2- 1.

Then dx=2*t*dt

Then indefinite integral (t 2- 1) * t 2 * 2 * dt.

Then open the two parts to integrate.

The final result is 2/5 * (x+1) 5-2/3 * (x+1) 3.