Question

Use any combination of integration techniques to evaluate the following integrals. You must show all of your steps!! 1. $\int x^3 e^{2x} dx$ 2. $\int x^3 \sqrt{4 - x^2} dx$ 3. $\int \frac{1}{x^2 - 2x - 15} dt$

          Use any combination of integration techniques to evaluate the following integrals. You must show all of your steps!!
1. $\int x^3 e^{2x} dx$
2. $\int x^3 \sqrt{4 - x^2} dx$
3. $\int \frac{1}{x^2 - 2x - 15} dt$

Use any combination of integration techniques to evaluate the following integrals. You must show all of your steps!!
1. ∫ x^3 e^2x dx
2. ∫ x^3 √(4 - x^2) dx
3. ∫(1)/(x^2 - 2x - 15) dt

Added by Jillian F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Enkhzaya Enkhtaivan

06/06/2019

Step 1

First, we factor the denominator: $x^2-2x-15 = (x-5)(x+3)$ Then, we can write the integrand as: $\frac{1}{x^2-2x-15} = \frac{A}{x-5} + \frac{B}{x+3}$ where A and B are constants. Show more…

Show all steps

Thanks for your feedback!

inite Use any combination of integration techniques to evaluate the following integrals. You must show all of your steps!! 1. $\int x^3e^{2x} dx$ 2. $\int x^3\sqrt{4-x^2} dx$ 3. $\int \frac{1}{x^2-2x-15} dt$