   Chapter 8, Problem 11RE

Chapter
Section
Textbook Problem

Using Integration by Parts In Exercises 9–16, use integration by parts to find the indefinite integral. ∫ e 2 x sin 3 x   d x

!
To determine

To calculate: The value of the integral e2xsin3xdx using integration by parts.

Explanation

Given:

The integral e2xsin3xdx

Formula used:

In integration by parts, there are two functions u and v,

uv=uv+vu

Calculation:

Let the value of u and v are

u=sin3x,v=e2x

The integral is solved as,

e2xsin3xdx=e2xsin3xdx+(sin3xdx)ddxe2xdx=13cos3x+23e2xcos3xdx=13cos3x+23[13e2xsin3x23<

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