Find using integration by substitution.

Question

Find  using integration by substitution.

Quizplus · Accepted Answer

Let u = 8x^2 + 9, then du/dx = 16x
dx = du/16x
Substituting this in the integral, we get:

Integral [(x+1)(8x^2+9)^2]dx
= Integral [(x+1)(u)^2]dx/16x 
= (1/16) * Integral [(x+1)u^2]du

Now, expanding the integrand and simplifying, we get:

(1/16) * Integral [(8x^3 + 17x^2 + 9x + 1)u^2]du 
= (1/16) * [(8/21)u^3 + (17/30)u^2 + (9/11)u + C]

Substituting back for u, we get:

(1/16) * [(8/21)(8x^2 + 9)^3 + (17/30)(8x^2 + 9)^2 + (9/11)(8x^2 + 9) + C]

Simplifying this expression gives us:

(64/441)(8x^2 + 9)^3 + (34/165)(8x^2 + 9)^2 + (9/176)(8x^2 + 9) + C

Therefore, the answer is 11eb69ff_feac_8ca5_af94_1f3e66c1d1ef_TB8190_11.

Find Using Integration by Substitution