find-e-x-sinxdx-

Question Number 172012 by Mikenice last updated on 23/Jun/22

f i n d

\int e^{x} s i n x d x

Answered by puissant last updated on 23/Jun/22

J = \int e^{x} s i n x d x

{\begin{cases} u^{'} = e^{x} \\ v = s i n x \end{cases} \Rightarrow {\begin{cases} u = e^{x} \\ v^{'} = c o s x \end{cases}

J = e^{x} s i n x - \int e^{x} c o s x d x

L = \int e^{x} c o s x d x

{\begin{cases} u^{'} = e^{x} \\ v = c o s x \end{cases} \Rightarrow {\begin{cases} u = e^{x} \\ v^{'} = - s i n x \end{cases}

L = e^{x} c o s x + \int e^{x} s i n x d x

\Rightarrow J = e^{x} s i n x - e^{x} c o s x - J

\Rightarrow J = \frac{e^{x}}{2} s i n x - \frac{e^{x}}{2} c o s x + C

Facebook Tweet Pin