Class 12MathematicsChapter 7: Integrals

7.2 Standard Integrals

Table of standard integral formulas for common functions.

7.2 Standard Integrals

Function	Integral
$\int x^n\,dx$	$\dfrac{x^{n+1}}{n+1} + C, \quad n \neq -1$
$\int \dfrac{1}{x}\,dx$	$\ln\lvert x \rvert + C$
$\int e^x\,dx$	$e^x + C$
$\int a^x\,dx$	$\dfrac{a^x}{\ln a} + C$
$\int \sin x\,dx$	$-\cos x + C$
$\int \cos x\,dx$	$\sin x + C$
$\int \sec^2 x\,dx$	$\tan x + C$
$\int \csc^2 x\,dx$	$-\cot x + C$
$\int \sec x \tan x\,dx$	$\sec x + C$
$\int \csc x \cot x\,dx$	$-\csc x + C$

7.1 Introduction

Integration as the inverse process of differentiation and the constant of integration.

7.3 Integration by Substitution

Method of substitution for integrating composite functions, with worked example.

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7.2 Standard Integrals