# Evaluate the integral using the indicated substitution. \int\cos^{2}x \sin xdx,\ u=\cos x

Evaluate the integral using the indicated substitution.
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Layton
Step 1
Consider the integrals,
$\int {\mathrm{cos}}^{2}x\cdot \mathrm{sin}xdx$...(1)
Let, $u=\mathrm{cos}x$
$du=-\mathrm{sin}xdx$
Step 2
Substitute all value in equation (1) then,
$\int {\mathrm{cos}}^{2}x\cdot \mathrm{sin}x\cdot dx=\int {u}^{2}\left(-du\right)$
$=-\int {u}^{2}du$
$=-\frac{{u}^{3}}{3}+C$
Substitute back, $u=\mathrm{cos}x$
$\int {\mathrm{cos}}^{2}x\cdot \mathrm{sin}x\cdot dx=-\frac{1}{3}{\mathrm{cos}}^{3}x+C$
Jeffrey Jordon