Mathematical formulas

Calculus II

Subjects Home Search Guide

Sections

1Notation, domains and conventions
2Indefinite integral and properties
3Definite integral and Fundamental Theorem of Calculus
4Substitution method
5Integration by parts
6Trigonometric integrals
7Trigonometric substitution and quadratic radicals
8Rational functions and partial fractions
9Improper integrals
10Applications of the integral
11Numerical integration
12Parametric curves
13Polar coordinates
14Sequences and series
15Power series and Taylor series
16Elementary differential equations
17Guide to choosing a method
AAppendix A: extensive table of antiderivatives
BAppendix B: useful equivalences

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Subjects
Calculus II
A.3. Inverse trigonometric integrals
Formula

A.3. Inverse trigonometric integrals

Formula

In A.3. Inverse trigonometric integrals

Formula

\int arctan u d u = u arctan u - \frac{1}{2} ln (1 + u^{2}) + C

Variables

$C$ Constant real de integración
$u$ Variable auxiliar de sustitución
$d u$ Diferencial respecto de $u$
$ln$ Logaritmo natural

Conditions

$ln (1 + u^{2}) + C$

Related formulas

Related
Formula
$\int arccos u d u = u arccos u - 1 - u^{2} + C$
Open formula Open in section
Related
A.3.2 Product with $u$
$\int u arcsin u d u = \frac{2 u ^{2} - 1}{4} arcsin u + \frac{u 1 - u ^{2}}{4} + C$
Open formula Open in section
Related
A.3.1 Direct integrals
$\int arcsin u d u = u arcsin u + 1 - u^{2} + C$
Open formula Open in section
Related
Formula
$\int u arctan u d u = \frac{u ^{2} + 1}{2} arctan u - \frac{u}{2} + C$
Open formula Open in section
Related
A.3.3 General powers ( $n \neq = - 1$ )
$\int u^{n} arcsin u d u = \frac{1}{n + 1} [u^{n + 1} arcsin u - \int \frac{u ^{n + 1} d u}{1 - u ^{2}}]$
Open formula Open in section
Related
Formula
$\int u^{n} arccos u d u = \frac{1}{n + 1} [u^{n + 1} arccos u + \int \frac{u ^{n + 1} d u}{1 - u ^{2}}]$
Open formula Open in section
Related
Formula
$\int u^{n} arctan u d u = \frac{1}{n + 1} [u^{n + 1} arctan u - \int \frac{u ^{n + 1} d u}{1 + u ^{2}}]$
Open formula Open in section