What is the integral of $int sin^3(x)cos^4(x) dx$ ?

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Answer 1 · 2016-08-26T19:13:13

$int sin^3(x)cos^4(x) dx = -1/5cos^5(x)+1/7cos^7(x) + C$

$int sin^3(x)cos^4(x) dx$

but

$sin^3(x)cos^4(x) =(1-cos^2(x))cos^4(x) sin(x)$
$=cos^4(x) sin(x)-cos^6(x) sin(x)$

then

$int sin^3(x)cos^4(x) dx = int(cos^4(x) sin(x)-cos^6(x) sin(x))dx$
$=-1/5cos^5(x)+1/7cos^7(x) + C$

What is the integral of int sin^3(x)cos^4(x) dxint sin^3(x)cos^4(x) dx?