Evaluate the integral of the product of x squared and the cube of the quantity x cubed plus 1, dx.

Question

Evaluate .

A. 

B.   C.  D. None of these

Answer 1

To evaluate the integral of x² (x³+1)dx let x³ +1 = u so that du = 3x²dx where x²dx = du/3. So the integral becomes ∫u³du/3 +C and this becomes u⁴/12 +C. Replacing u the integral is (x³ +1)⁴/12 +C which is answer B.