Use substitution to find the integral .

Question

Use substitution to find the integral  . ​

Quizplus · Accepted Answer

Let u = x^3 + 5. Then du/dx = 3x^2 and dx = du/3x^2. Substituting into the integral, we get:

∫ 11e^(u) du/3x^2 = (11/3) ∫ e^(u) dx/x^2

Using the formula for integrating e^(ax), we get:

(11/3) ∫ e^(u) dx/x^2 = -(11/3) (1/x)e^(u) + (11/3) ∫ e^(u) dx/x

Substituting back in for u and simplifying, we get:

-(11/3) (1/x)e^(x^3+5) + (11/9) e^(x^3+5) + C

where C is the constant of integration.

Therefore, the answer is D, 11eac44f_ec70_3b8c_bedf_bb2949f8de63_TB7497_11.

Use Substitution to Find the Integral