EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Indefinite Integration>JEE Main - 10th April 2019 Shift 1>Q 29

MEDIUM

JEE Main

IMPORTANT

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If $\int \frac{d x}{{(x^{2} - 2 x + 10)}^{2}} = A (\tan^{- 1} (\frac{x - 1}{3}) + \frac{f (x)}{x^{2} - 2 x + 10}) + C$ , then (where $C$ is a constant of integration)

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Important Questions on Indefinite Integration

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Indefinite Integration>JEE Main - 10th April 2019 Shift 2>Q 30

If

\int x^{5} e^{- x^{2}} d x = g (x) e^{- x^{2}} + c

, where

c

is a constant of integration, then

g (- 1)

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Indefinite Integration>JEE Main - 10th January 2019 Shift 1>Q 31

Let,

n \geq 2

be a natural number and

0 < θ < \frac{π}{2} .

Then

\int \frac{{(s i n^{n} θ - s i n θ)}^{\frac{1}{n}} c o s θ}{s i n^{n + 1} θ} d θ,

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Indefinite Integration>JEE Main - 10th January 2019 Shift 2>Q 32

If

\int x^{5} e^{- 4 x^{3}} d x = \frac{1}{48} e^{- 4 x^{3}} f (x) + C

, where

C

is a constant of integration, then

f (x)

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Indefinite Integration>JEE Main - 12th April 2019 Shift 1>Q 33

The integral

\int \frac{2 x^{3} - 1}{x^{4} + x} d x

, is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Indefinite Integration>JEE Main - 12th April 2019 Shift 2>Q 34

Let

α \in (0, \frac{π}{2})

, be constant. If the integral

\int \frac{t a n x + t a n α}{t a n x - \tan α} d x = A (x) c o s 2 α + B (x) s i n 2 α + C

, where C is a constant of integration, then the functions

A (x)

and

B (x)

are respectively

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Indefinite Integration>JEE Main - 12th January 2019 Shift 1>Q 35

The integral

\int c o s (lnx) d x

, is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Indefinite Integration>JEE Main - 12th January 2019 Shift 2>Q 36

The integral

\int \frac{3 x^{13} + 2 x^{11}}{{(2 x^{4} + 3 x^{2} + 1)}^{4}} d x

, is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Indefinite Integration>JEE Main - 8th April 2018>Q 37

The integral

\int \frac{\sin^{2} x \cos^{2} x}{{(\sin^{5} x + \cos^{3} x \sin^{2} x + \sin^{3} x \cos^{2} x + \cos^{5} x)}^{2}} d x

, is equal to

(where

C

is the constant of integration).