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integral (2+3x^2)/ ( x^2 + (1+x^2) ) dx How to do this sum ??

integral (2+3x^2)/ ( x^2 + (1+x^2) ) dx
 
 
How to do this sum ??

Grade:12

1 Answers

BALAJI ANDALAMALA
askIITians Faculty 78 Points
8 years ago
\int \frac{(2+3x^2)}{(x^2+(1+x^2))}dx = \int \frac{(2+3x^2)}{1+2x^2}dx
=\int \frac{3}{2} dx+ \int \frac{1}{2(1+2x^2)}dx
= \frac{3}{2}x + \frac{1}{4}tan^{-1}{\sqrt{2} x}+c

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