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Evaluate: inte^(2x)cos^2x\ dx...

Evaluate: `inte^(2x)cos^2x\ dx`

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`I=int e^{2 x} cos ^{2} x d x=int e^{2 x}(frac{1+cos 2 x}{2}) d x `
` =frac{1}{2} int e^{2 x} d x+frac{1}{2} int e^{2 x} cos 2 x d x `
` I=frac{e^{2 x}}{4}+frac{1}{2} I_{1} `
` I_{1}=int e_{1}^{2 x} cos 2 x d x`
` I_{1}=e^{2 x} frac{sin 2 x}{2}-int 2 e^{2 x} frac{sin 2 x}{2} d x `
` =e^{2 x} frac{sin 2 x}{2}-[e^{2 x}(frac{-cos 2 x}{2}). `
` I_{1}=frac{e^{2 x}}{4}[sin 2 x+cos 2 x]+c `
` I_{1}=e^{2 x} frac{sin 2 x}{2}+e^{2 x} frac{cos 2 x}{2}] I_{1}=frac{e^{2 x}}{2}[sin 2 x+cos 2 x]+c `
` ...
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