$\int \frac{5 x - 2}{1 + 2 x + x^{2}} d x$

Open in App

Solution

$\int \frac{5 x - 2}{1 + 2 x + x^{2}} d x$

$= \int \frac{5 x - 2}{{(x + 1)}^{2}}$

put $x + 1 = d$
$d x = d t$

$= \int \frac{5 (t - 1) - 2}{t^{2}} d t$

$5 log t + \frac{7}{t} x$

$= 5 (\frac{1}{t} d t - 7) \frac{1}{t^{2}} d t$

$= 5 log t + \frac{7}{t} + c$

$= 5 log (x t_{1}) + \frac{7}{n + 1} + c$

Suggest Corrections

Similar questions

\int \frac{5 x + 7}{\sqrt{3 - 2 x - x^{2}}} d x

\frac{1}{2} \int \frac{2 x}{{(1 + x)}^{2}} d x

\int \frac{2 x}{(1 + x^{2})} d x

\int (2^{x} + 2^{- x})^{2} d x =

\int (2 x - 1) \sqrt{1 + x - x^{2}} d x

Join BYJU'S Learning Program