Use the table of integrals to find the integral.

Name: Use the table of integrals to find the integral.
Brand: Quizplus
Rating: 4.8 (40 reviews)

Question

Use the table of integrals to find the integral. ​  ​

Quizplus · Accepted Answer

The integral is ∫(x^3)/sqrt(1-x^2) dx. Using Table II, we see that the substitution u = 1 - x^2 works, and we have du/dx = -2x. Solving for dx, we get dx = -du/(2x). Substituting into the integral and simplifying, we get:

∫(x^3)/sqrt(1-x^2) dx = -1/2 ∫u^(-1/2) du = -√u + C = -√(1-x^2) + C

Therefore, the answer is B.

Use the Table of Integrals to Find the Integral