Question

Evaluate ∫cos³ xsin⁴ xdx.

Answer 1

Answer:

$\int \:cos^3x\cdot sin^4xdx=\int \:cosx\cdot cos^2x\cdot sin^4xdx=\int \:cosx\left(1-sin^2x\right)sin^4xdx=\int \:\frac{cosx}{cosx}\left(1-u^2\right)u^4du=\int \:u^4-u^6=\frac{u^5}{5}-\frac{u^7}{7}+C=\frac{1}{5}sin^5x-\frac{1}{7}sin^7x+C$

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Step-by-step explanation: