∫(1+log x)^2xdx Put, 1+log x = t 1x dx = dt Now, ∫(1 + log x)^2x dx = ∫ t^2 dt = t^33 + c = (1+log x)^33 + c ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Special Integrals - 1

Solve ∫1+lo...

Question

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

Open in App

Solution

$\int \frac{(1 + log x)^{2}}{x} d x$
Put, $1 + log x = t$

$⟹ \frac{1}{x} d x = d t$

Now, $\int \frac{(1 + log x)^{2}}{x} d x$

$= \int t^{2} d t$

$= \frac{t^{3}}{3} + c$

$= \frac{(1 + log x)^{3}}{3} + c$

Suggest Corrections

Similar questions

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

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

Integrate the following functions.
$\int \frac{(1 + l o g x)^{2}}{x} d x .$

\int {(\log x)}^{2} \cdot x d x

\int \frac{(l o g x)^{2}}{x} d x

Join BYJU'S Learning Program