Evaluate the integral using the given substitution

Question

∫ 6(2X-1)^-3 dx, u = 2x -1

(2x-1)^-2 + C

-3/4(2x-1)^-4 + C

-3(2x-1)^-2 +C

-3/2(2x-1)^-2 +C

Answer 1

u=2x - 1

du=2dx

∫6(2x - 1)^-3dx becomes

(1/2)∫6u^-3du. The (1/2) has to balance the change of dx to 2dx. We use 2dx to express the integral with respect to u. 2x is equivalent to du.

Integrate in turns of u now.

(1/2)*6*u^-3+1/(-3+1) + C

(3/-2)u^-2 + C

rewrite in terms of x

-(3/2)(2x - 1)^-2 + C is the final answer.