Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Integration (p-1)1 Mark
Question
Evalute : $\int\left(e^x+e^{-x}\right)^2\left(e^x-e^{-x}\right) d x$
✓
Answer
Let $I=\int\left(e^x+e^{-x}\right)^2\left(e^x-e^{-x}\right) d x$ Put $e^x+e^{-x}=t$ $ \begin{aligned} & \therefore\left(e^x-e^{-x}\right) d x=d t \\ & \begin{aligned} \therefore I & =\int t^2 d t=\frac{t^3}{3}+c \\ & =\frac{\left(e^x+e^{-x}\right)^3}{3}+c . \end{aligned} \end{aligned} $
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