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Question Number 203573 by sonukgindia last updated on 22/Jan/24

Answered by esmaeil last updated on 22/Jan/24

$$\int -e^{cosx}(1-{cos}^{2}x-cosx)dx$$$$\int -e^{cosx}({sin}^{2}x-cosx)dx=$$$$\int -e^{cosx}{sin}^{2}xdx+\int {cosxe}^{cosx}dx=\mathrm{{\rm Y}}$$$$-e^{cosx}sinxdx=dv\to$$$$v=e^{cosx}sinx=u\to cosxdx=du\to$$$$\mathrm{{\rm Y}}=sinx\left(e^{cosx}\right)-\int e^{cosx}coscdx$$$${+\int e^{cosx}cosxdx=sinx\left(e^{cosx}\right)]}_0^1=$$$$sin\left(1\right)e^{cos1}$$$$$$$$$$

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