Evaluate the following integrals: ^5x dx - Vidyadip

Question

Evaluate the following integrals:
$\int\sin^5\text{x}\cos\text{x dx}$

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Answer

$\int\sin^5\text{x}\cos\text{x dx}$
$\text{Let }\sin\text{x}=\text{t}$
$\Rightarrow\cos\text{x}=\frac{\text{dt}}{\text{dx}}$
$\Rightarrow\cos\text{x dx}=\text{dt}$
$\text{Now,}\int\sin^5\text{x}\cos\text{x dx}$
$=\int\text{t}^5\text{dt}$
$=\frac{\text{t}^6}{6}+\text{C}$
$=\frac{1}{6}\sin^6\text{x}+\text{C}$

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