Mathematics

Write a value of 
$$\int { { e }^{ x }\left( \sin { x } +\cos { x }  \right)  } dx$$


SOLUTION
$$I=\displaystyle\int{{e}^{x}\left(\sin{x}+\cos{x}\right)dx}$$

It is of the form $$\displaystyle\int{{e}^{x}\left(f\left(x\right)+{f}^{\prime}{\left(x\right)}\right)dx}={e}^{x}f\left(x\right)+c$$

Put $$f\left(x\right)=\sin{x}$$ and $${f}^{\prime}{\left(x\right)}=\cos{x}$$

$$\therefore\,\displaystyle\int{{e}^{x}\left(\sin{x}+\cos{x}\right)dx}={e}^{x}\sin{x}+c$$      ......where $$c$$ is the constant of integration.
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Subjective Medium Published on 17th 09, 2020
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