Evaluate: `inte^(a x)cos(b x+c)\ dx`

Explanation

Let, `I=int e_{I}^{a x} cos (b x+c) d x.`

Integrating by parts, we get
`

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

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