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# Integration by Parts - Indefinite Integration JEE Notes | EduRev

## JEE : Integration by Parts - Indefinite Integration JEE Notes | EduRev

The document Integration by Parts - Indefinite Integration JEE Notes | EduRev is a part of the JEE Course Mathematics (Maths) Class 12.
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Integration By Parts
dx where u & v are differentiable functions.

Note : While using integration by parts, choose u & v such that
(a)  dx v is simple &

(b)  dx is simple to integrate.

This is generally obtained, by keeping the order of u & v as per the order of the letter in ILATE, where

I – Inverse function
L – Logarithmic function
A – Algebraic function
T – Trigonometric function
E – Exponential function

Ex.38 Integrate xlog x

Sol.

Ex.39 Evaluate dx

Sol.

Put sec–1 x = t so that

Then the given integral  =

= t (log t – log e) + c  = sec–1 x (log (sec–1 x) – 1) + c

Ex.40 Evaluate dx.

Sol.

Put x = cos θ so that dx = - sin θ dθ. the given integral

Ex.41 Evaluate

Sol.

We have

[ x3 = x(x2 + 1) - x]

integrating by parts taking x2 as the second function

Ex.42 Evaluate dx.

Sol.

(put, 2x + 2 = 3 tanθ ⇒ 2 dx = 3 sec2θ dθ )

Ex.43 If

Sol.

REMEMBER THIS

Integrating by parts taking sin bx as the second function,

Again integrating by parts taking cos bx as the second function, we get

Transposing the term -a2/b2 I to the left hand side, we get

Ex.44 Evaluate

Sol.

Ex.45 Evaluate

Sol.

x where f(x) = tan x = ex f(x) + c = ex tanx + c

Ex.46 Evaluate

Sol.

using, previous example

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## Mathematics (Maths) Class 12

209 videos|222 docs|124 tests

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