Question Bank [2022] — Maths STD 12 Science — Question
Maharashtra BoardEnglish MediumSTD 12 ScienceMathsQuestion Bank [2022]2 Marks
Question
$\int \frac{ e ^x \log \left(\sin e ^x\right)}{\tan e ^x} d x$
✓
Answer
$ \text { Let } I =\int \frac{ e ^x \cdot \log \left(\sin e ^x\right)}{\tan \left( e ^x\right)} d x$
$=\int e ^x \cdot \log \left(\sin e ^x\right) \cdot \cot \left( e ^x\right) d x $
Put $\log \left(\sin e^x\right)=t$
Differentiating w.r.t. $x_r$ we get
$ \frac{\cos e ^x}{\sin e ^x} \cdot e ^x d x= dt$
$\therefore e ^x \cdot \cot e ^x d x= dt$
$\therefore l =\int t \cdot dt =\frac{ t ^2}{2}+ c$
$\therefore I =\frac{\left[\log \left(\sin e ^x\right)\right]^2}{2}+ c $
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