Mathematics | MHT CET 2020 | Discussion Page

1)

$\int \frac{dx}{x^{2}+4x+13}=$

A)

$\frac{1}{3}\tan^{-1}\left(\frac{x+2}{3}\right)+C$

B)

$\frac{1}{6}\tan^{-1}\left(\frac{x-1}{x+5}\right)+C$

C)

$3\tan^{-1}\left(\frac{x+2}{3}\right)+C$

D)

$\frac{1}{6}\tan^{-1}\left(\frac{x+2}{3}\right)+C$

Option A

We have,

l= $\int \frac{dx}{x^{2}+4x+13}$

l= $\int \frac{dx}{x^{2}+4x+4+9}$ = $\int \frac{dx}{(x+2)^{2}+(3)^{2}}$

l= $\frac{1}{3}\tan^{-1}\left(\frac{x+2}{3}\right)+C$

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