Question

Need some help with the one......Evaluate the integral x^3(x^4+5)^1/2 dx

Answer 1

Let u = x^4 +5 , du= 4x^3 dx , dx= 1/4x^3
When you plug this back into the integral you will get:
integral ( (u)^1/2 /4 du) You can then pull the 1/4 out of the integral leaving just u^1/2 du in the integral. Using the power rule this can be evaluated to u^3/2 which we will replace back with x^4 +5, giving us the answer:
1/4 (x^4+5) ^3/2 +C