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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.6
Integrate the functions in Exercises 134 to 155.
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Question : 149 of 271
Marks: +1, -0
ex(sin⁡x+cos⁡x)e^x (\sin x + \cos x)
Solution:  
Let I=∫ex(sin⁡x+cos⁡x)dxI=\int e^x (\sin x + \cos x)dx
Put exsin⁡x=te^x \sin x = t
⇒(excos⁡x+sin⁡x.ex)dx=dt\Rightarrow (e^x\cos x+\sin x.e^x)dx=dt
⇒ex(sin⁡x+cos⁡x)dx=dt\Rightarrow e^x(\sin x+\cos x)dx=dt
∴I=∫dt=t+C\therefore I=\int dt = t+C =exsin⁡x+C=e^x\sin x+C
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