First slide

Methods of integration

Question

$I f I_{n} = \int {(\ln x)}^{n} d x t h e n I_{n} + n I_{n - 1} =$

Easy

A

$\frac{{(\ln x)}^{n}}{x}$
B

$x {(\ln x)}^{n - 1}$
C

$x {(\ln x)}^{n}$
D

None of these

Solution

$\begin{array}{l} I_{n} = \int {(\ln x)}^{n} .1 d x \\ (I n t e g r a t i n g b y p a r t s) \\ = x {(\ln x)}^{n} - \int \frac{x (n) {(\ln x)}^{n - 1}}{x} d x \\ = x {(\ln x)}^{n} - n I_{n - 1} \\ ∴ I_{n} + n I_{n - 1} = x {(\ln x)}^{n} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App