   Chapter 7.R, Problem 24E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ e x cos x d x

To determine

To Find:excosxdx

Explanation

Formula Used:uvdt=uvdtu'(vdt)dt

Calculation:

Here, the integrand is the product of tow functions with known integrals. So, the one method which comes first in mind is the integration by parts.

Let I=excosx and integrate it to get

I=excosxdx  =excosxdxddx(ex)(cosxdx)dx  =exsinxexsinxdx

Again, use integration by parts for the remaining integral exsinxdx but remember, don’t change the order of integration that is, take u=ex and v=sinx and then integrate to have

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