Indefinite Integration formulas

Every formula JEE Advanced expects you to know for Indefinite Integration, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

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Formulas: 34
Subject: Mathematics
Exam: JEE Advanced
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Indefinite Integration, every formula

34 formulas, typeset and free. Print it, or keep it open beside your practice.

Power rule
$\int x^{n} d x = \frac{x ^{n + 1}}{n + 1} + C, n \neq = - 1$
Reciprocal
$\int \frac{1}{x} d x = ln ∣ x ∣ + C$
Exponential
$\int e^{x} d x = e^{x} + C$
General exponential
$\int a^{x} d x = \frac{a ^{x}}{ln a} + C$
a>0, a≠1
Sine
$\int sin x d x = - cos x + C$
Cosine
$\int cos x d x = sin x + C$
sec^2
$\int sec^{2} x d x = tan x + C$
cosec^2
$\int csc^{2} x d x = - cot x + C$
sec·tan
$\int sec x tan x d x = sec x + C$
Integral of tan
$\int tan x d x = ln ∣ sec x ∣ + C$
Integral of sec
$\int sec x d x = ln ∣ sec x + tan x ∣ + C$
arcsin form
$\int \frac{d x}{1 - x ^{2}} = sin^{- 1} x + C$
arctan form
$\int \frac{d x}{1 + x ^{2}} = tan^{- 1} x + C$
Linear substitution
$\int f (a x + b) d x = \frac{F ( a x + b )}{a} + C$
F'=f
Log-derivative rule
$\int \frac{f ^{'} ( x )}{f ( x )} d x = ln ∣ f (x) ∣ + C$
Power of a function
$\int [f (x)]^{n} f^{'} (x) d x = \frac{[ f ( x ) ] ^{n + 1}}{n + 1} + C, n \neq = - 1$
Root of a function
$\int \frac{f ^{'} ( x )}{f ( x )} d x = 2 f (x) + C$
arcsin (a)
$\int \frac{d x}{a ^{2} - x ^{2}} = sin^{- 1} \frac{x}{a} + C$
arctan (a)
$\int \frac{d x}{a ^{2} + x ^{2}} = \frac{1}{a} tan^{- 1} \frac{x}{a} + C$
1/(x^2-a^2)
$\int \frac{d x}{x ^{2} - a ^{2}} = \frac{1}{2 a} ln \frac{x - a}{x + a} + C$
1/(a^2-x^2)
$\int \frac{d x}{a ^{2} - x ^{2}} = \frac{1}{2 a} ln \frac{a + x}{a - x} + C$
1/sqrt(x^2+a^2)
$\int \frac{d x}{x ^{2} + a ^{2}} = ln x + x^{2} + a^{2} + C$
1/sqrt(x^2-a^2)
$\int \frac{d x}{x ^{2} - a ^{2}} = ln x + x^{2} - a^{2} + C$
sqrt(a^2-x^2)
$\int a^{2} - x^{2} d x = \frac{x}{2} a^{2} - x^{2} + \frac{a ^{2}}{2} sin^{- 1} \frac{x}{a} + C$
sqrt(x^2+a^2)
$\int x^{2} + a^{2} d x = \frac{x}{2} x^{2} + a^{2} + \frac{a ^{2}}{2} ln x + x^{2} + a^{2} + C$
Integration by parts
$\int u v d x = u \int v d x - \int (\frac{d u}{d x} \int v d x) d x$
first fn by ILATE
e^x [f+f']
$\int e^{x} (f (x) + f^{'} (x)) d x = e^{x} f (x) + C$
e^x·(sin/cos)
$\int e^{a x} sin b x d x = \frac{e ^{a x}}{a ^{2} + b ^{2}} (a sin b x - b cos b x) + C$
x^n·ln x
$\int x^{n} ln x d x = \frac{x ^{n + 1}}{n + 1} (ln x - \frac{1}{n + 1}) + C$
n≠-1
Integral of arcsin
$\int sin^{- 1} x d x = x sin^{- 1} x + 1 - x^{2} + C$
Integral of arctan
$\int tan^{- 1} x d x = x tan^{- 1} x - \frac{1}{2} ln (1 + x^{2}) + C$
Reduction: sin^n
$I_{n} = \frac{- sin ^{n - 1} x cos x}{n} + \frac{n - 1}{n} I_{n - 2}$
I_n=∫sin^n x dx
Reduction: tan^n
$I_{n} = \frac{tan ^{n - 1} x}{n - 1} - I_{n - 2}$
I_n=∫tan^n x dx
Weierstrass substitution
$t = tan \frac{x}{2} : sin x = \frac{2 t}{1 + t ^{2}}, cos x = \frac{1 - t ^{2}}{1 + t ^{2}}, d x = \frac{2 d t}{1 + t ^{2}}$
for ∫dx/(a+b sin x) etc.

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Indefinite Integration formulas

Indefinite Integration, every formula

Power rule

Reciprocal

Exponential

General exponential

Sine

Cosine

sec^2

cosec^2

sec·tan

Integral of tan

Integral of sec

arcsin form

arctan form

Linear substitution

Log-derivative rule

Power of a function

Root of a function

arcsin (a)

arctan (a)

1/(x^2-a^2)

1/(a^2-x^2)

1/sqrt(x^2+a^2)

1/sqrt(x^2-a^2)

sqrt(a^2-x^2)

sqrt(x^2+a^2)

Integration by parts

e^x [f+f']

e^x·(sin/cos)

x^n·ln x

Integral of arcsin

Integral of arctan

Reduction: sin^n

Reduction: tan^n

Weierstrass substitution

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