A) \[{{e}^{x}}{{\sin }^{2}}x+c\]
B) \[{{e}^{x}}\sin x+c\]
C) \[{{e}^{x}}\sin 2x+c\]
D) None of these
Correct Answer: A
Solution :
\[\int_{{}}^{{}}{{{e}^{x}}\sin x(\sin x+2\cos x)dx}\] \[=\int_{{}}^{{}}{{{e}^{x}}{{\sin }^{2}}x\,dx}+\int_{{}}^{{}}{{{e}^{x}}2\sin x\,\cos xdx}\] \[=\int_{{}}^{{}}{{{e}^{x}}{{\sin }^{2}}x\,dx}+\int_{{}}^{{}}{{{e}^{x}}\sin 2x\,dx}\] \[={{e}^{x}}{{\sin }^{2}}x-\int_{{}}^{{}}{{{e}^{x}}\sin 2x\,dx}+\int_{{}}^{{}}{{{e}^{x}}\sin 2x\,dx\,+c}\] \[={{e}^{x}}{{\sin }^{2}}x+c.\] Aliter : \[\int_{{}}^{{}}{{{e}^{x}}({{\sin }^{2}}x+\sin 2x)dx={{e}^{x}}{{\sin }^{2}}x+c.}\]
You need to login to perform this action.
You will be redirected in
3 sec
