Techniques of Integration: Integration by Parts, Products of Powers of

Jaya Legge

Jaya Legge

Answered question

2021-10-04

Techniques of Integration: Integration by Parts, Products of Powers of Trigonometric Functions
Use integration by parts to integrate functions.
Integrate products of powers of trigonometric functions.
Evaluate
csc3xcot5xdx

Answer & Explanation

gotovub

gotovub

Skilled2021-10-05Added 98 answers

Step1
Given the integral
csc3xcot5xdx
To Evaluate the integral
I=csc3xcot5xdx
=cscxcotx{(csc2x{(cot2x})})dx
=cscxcotx{(csc2x{(csc2x1})2})dx
Step 2
Substitute
u=cscx
du=cscxcotxdx
I=u2{(u21})2du
I={(u62u4+u2})du
={[u772{(u55})+u33}]+c
=csc7x7+2csc5x5csc3x3+c

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