Indefinite Integral

Question

Consider the indefinite integral ∫x4(x5+5)5 dx:

This can be transformed into a basic integral by letting

u=    and

du= dx  

Performing the substitution yields the integral

∫ du  

Answer 1

Hello Jay,

If you let u = x⁵ + 5 (A)

then du = 5x⁴ dx (B)

to make it easier to visualize how to substitute, rewrite ∫x⁴(x⁵+5)⁵ dx as ∫(x⁵+5)⁵ x⁴dx

Based on equation (A), you should see that (x⁵+5)⁵ can be substituted as u⁵

Based on equation (B), you should see that x⁴dx can be substituted as du/5

I'll let you put it all together and finish the question. You got this.