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Home  >>  CBSE XII  >>  Math  >>  Model Papers

Evaluate : $ \int (cosec^2x-\cot\: x)e^x\: dx $

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1 Answer

Toolbox:
  • $\int e^x[f(x)+f'(x)]dx=e^x(f(x))+c$
Step 1:
$I=\int(cosec ^2x-\cot x)e^x dx$
Let $f(x)=-\cot x$
Then $f'(x)=-(-cosec^2 x)$
Step 2:
We know $\int e^x[f(x)+f'(x)]dx=e^x(f(x))+c$
$\therefore I=e^x(-\cot x)+c$
$\Rightarrow -e^x\cot x$+c
answered Oct 1, 2013 by sreemathi.v
 
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