   Chapter 4.5, Problem 47E

Chapter
Section
Textbook Problem

Finding an Indefinite Integral In Exercises 39-48, find the indefinite integral. ∫ csc 2 x cot 3 x   d x

To determine

To calculate: The value of the indefinite integral csc2xcot3xdx

Explanation

Given:

The indefinite integral is: csc2xcot3xdx.

Formula used:

The derivative of cotax is:

ddxcotax=acsc2ax

The integration of xn is:

xndx=xn+1n+1+C

The change of variable theorem for the indefinite integral:

If u=g(x). Then du=g'(x)dx.

Then, the integral will take the following form:

f(g(x))g'(x)dx=f(u)du=F(u)+C

Calculation:

Consider the provided indefinite integral,

csc2xcot3xdx

Let cotx=u. Then,

csc2x=dudxcsc2xdx=du

Now, put the value of csc2xdx and cotx in the provided indefinite integral

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