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trig integration? (1 Viewer)

Thread starter nfreidman
Start date Apr 28, 2012

N

nfreidman

New Member

#1

how do you integrate cube root of(sinx.cos^3x)

thanks

asianese

Σ

#2

Expand out the power, leaving
$\int \sqrt[3]{\sin x} \cos x dx\\ \text{Let}\, u=\sin x\\\therefore du=\cos x \,dx$
Integrate from there.

Carrotsticks

Retired

#3

$\int \sqrt[3]{\sin(x) \cos^3 (x)} dx \\\\ = \int \cos (x) \sqrt[3]{\sin(x)}dx \\\\ = \int \cos (x) \sin^{\frac{1}{3}} (x) dx \\\\ = \frac{3}{4} \sin^{\frac{4}{3}}(x) + C$

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