Integration Formula 1x

Integration can be used to find areas volumes central points and many useful things.

Integration formula 1x. The answer is that fx1x on mathbbr implies that there are constants c1c2inmathbbr such that fxlogxc1 for all x0 and fxlog xc2 for all x0. Integral of 1x2 using the integration formula the same rules apply treat n as 2. This page lists some of the most common antiderivatives. Our calculator allows you to check your solutions to calculus exercises.

1 x ta 1e t dt 58 z eax 2 dx i p 2 p a erf ix p a 59 z e ax 2 dx p 2 p a erf x p a 60 z xe ax 2 dx 1 2a e 61 z x2e ax 2 dx 1 4 r a3 erfx p a x 2a e 2 62 2014. Sec x tan x dx sec x c. The integral of many functions are well known and there are useful rules to work out the integral of more complicated functions many of which are shown here. Integration is the basic operation in integral calculuswhile differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions integration does not so tables of known integrals are often useful.

A dx ax c. 1 x ax b dx ax bn a n x b n 2 a n n forn n 2 ln x x b dx ax b ax b a a 2 2 2 1 ln x b dx ax b ax b a ax b a 2 1 1 2 1 2 1 n n x a n x b dx ax b a n n for n ax b n 2 2 2 3 1 2 ln 2 x ax b dx b ax b b ax b ax b a 2 2 2 3 1 2 ln. Sec 2 dx tan x c. X n dx x n1 n1c.

But it is often used to find the area underneath the graph of a function like this. 1 dx x c. Csc 2 dx cot x c. Cos x dx sin x c.

Sin x dx cos x c. N6 1 2 z 1 x dx lnjxj 3 z udv uv z vdu 4 z 1 ax b dx 1 a lnjax bj integrals of rational functions 5 z 1 x a2 dx 1 x a 6 z x andx x an1 n 1n6 1 7 z xx andx x an1n 1x a n 1n 2 8 z 1 1 x2 dx tan 1 x 9 z 1 a2 x2 dx 1 a tan 1 x a 1. The integral calculator lets you calculate integrals and antiderivatives of functions online for free. All common integration techniques and even special functions are supported.

This material is provided as is without warranty or representation about the accuracy correctness or. It helps you practice by showing you the full working step by step integration.