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Evaluate: int(sin^2x)/(cos^6x)\ dx...

Evaluate: `int(sin^2x)/(cos^6x)\ dx`

Text Solution

Verified by Experts

Dividing by `cos6x`
`int tan^2x sec^4xdx`
`tanx=t=>sec^2xdx=dt`
`=int t^2(1+t^2)dt`
`=int t^2 dt+int t^4dt`
`=frac{t^3}{3}+frac{t^5}{5}`
`=frac{tan^3x}{3}+frac{tan^5x}{5}`
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