Mathematics Crash Course JEE Advanced>Chapter 22 - Indefinite Integration>Exercise 1>Q 20

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IMPORTANT

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If a function $f : R \to R$ is defined as $f (x) = \int \frac{x^{8} + 4}{x^{4} - 2 x^{2} + 2} d x$ and $f (0) = 1$ , then which of the following is correct?

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Important Questions on Indefinite Integration

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 22 - Indefinite Integration>Exercise 1>Q 21

The value of

\int \frac{1}{{[(x - 1)^{3} (x + 2)^{5}]}^{\frac{1}{4}}} d x

is equal to

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Mathematics

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Mathematics Crash Course JEE Advanced>Chapter 22 - Indefinite Integration>Exercise 1>Q 22

\int x \sqrt{\frac{a^{2} - x^{2}}{a^{2} + x^{2}}} d x =

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Mathematics

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Mathematics Crash Course JEE Advanced>Chapter 22 - Indefinite Integration>Exercise 1>Q 23

Let

f (x) = \frac{x}{{(1 + x^{n})}^{\frac{1}{n}}}

for

n \geq 2

and

g (x) = \underset{f occurs n times}{\underset{⏟}{(f o f o f o f . . . . . o f)}} (x)

. Then,

\int x^{n - 2} g (x) d x

equals (where

K

is an integration constant)

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Mathematics

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Mathematics Crash Course JEE Advanced>Chapter 22 - Indefinite Integration>Exercise 1>Q 24

Let

I = \int \frac{e^{x}}{e^{4 x} + e^{2 x} + 1} d x, J = \int \frac{e^{- x}}{e^{- 4 x} + e^{- 2 x} + 1} d x

. Then, for an arbitrary constant

C

, the value of

J - I

equals

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 22 - Indefinite Integration>Exercise 1>Q 25

\int \frac{x + 2}{(x^{2} + 3 x + 3) \sqrt{x + 1}} d x =

, (Where

c

is constant of integration)

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 22 - Indefinite Integration>Exercise 1>Q 26

\int \frac{\cos 5 x + \cos 4 x}{1 - 2 \cos 3 x} d x =

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Mathematics

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Mathematics Crash Course JEE Advanced>Chapter 22 - Indefinite Integration>Exercise 1>Q 27

\int \sin^{- 1} \sqrt{\frac{x}{a + x}} d x =

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 22 - Indefinite Integration>Exercise 1>Q 28

If

f (\frac{1 - x}{1 + x}) = x

and

g (x) = \int f (x) d x

, then