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## Homework Statement

Evaluate

integral sin^(-3/2)(x)cos^3(x) dx

## Homework Equations

tan(x)=sin(x)/cos(x)

sin^2(x)+cos^2(x)=1

sin^2(x)=(1-cos(x))/2

cos^2(x)=(1+cos(2x))/2

integral cos(x)dx = sin(x) + c

integral sin(x)dx = -cos(x) + c

d/dx sin(x) = cos(x)

d/dx cos(x) = -sin(x)

a^m/a^n=a^(m-n)

a^m*a^n=a^(m+n)

sin(x)=(e^(ix)-e^(-ix))/(2i)

cos(x)=(e^(ix)+e^(-ix))/2

tan(x)=sin(x)/cos(x)

cis(x)=cos(x)+i*sin(x)=e^(ix)

cis(-x)=cos(x)-i*sin(x)=e^(-ix)

e^(i*pi)+1=0

## The Attempt at a Solution

I'm at a lost as to how even to being...

I tried using sin^2(x)+cos^2(x)=1

I tried using some of the double angle formulas

every single time I get to the point were I don't know how to proceed

MATLAB answer:

>> int(cos(x)^3/sin(x)^(3/2))

Warning: Explicit integral could not be found.

ans =

int(cos(x)^3/sin(x)^(3/2), x)

Wolfram Alpha answer:

-40/9 F(1/4 (pi-2 x)|2)-2/9 sqrt(sin(x)) (2 cos(x)+3 x (sin(x)+3 csc(x)))+constant

My answer:

Don't even know how to proceed after a couple of steps

Back of the book:

Only odd answers are given... this is problem #16

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