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Question Number 74210 by malikmasood3535@gmail.com last updated on 20/Nov/19

$$\int e^t\cos e^{t}dt$$

Answered by mind is power last updated on 20/Nov/19

$$\int e^{t}cos\left(t\right)dt=sin\left(e^t\right)+c$$$$pathu=e^t\Rightarrow du=e^{t}dt$$$$\Rightarrow e^{t}cos\left(t\right)dt=cos\left(e^t\right).\left(e^{t}dt\right)=cos\left(u\right)du$$$$\int cos\left(u\right)du=sin\left(u\right)+c,subsituteuby{e}^{t}weget$$$$=sin\left(e^t\right)+c,c\in \mathbb{R}$$

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