# Free Step-by-Step Integral Solver

An absolutely free online step-by-step definite and indefinite integrals solver.

Integral
 dx

Use latex commands:
* is multiplication
oo is $\infty$
pi is $\pi$
x^2 is x2
sqrt(x) is $\sqrt{x}$
sqrt[3](x) is $\sqrt[3]{x}$
(a+b)/(c+d) is $\frac{a+b}{c+d}$

#### Common Integrals

$\int 0dx = \text{const}$

$\int\ dx = x + \text{const}$

$\int kdx = kx + \text{const}$

$\int x^n\ dx = \frac{1}{n+1}x^{n+1} + \text{const}$ here n≠-1

$\int \frac{1}{x}\ dx = \int x^{-1}\ dx = \ln|x| + \text{const}$

$\int x^{-n}\ dx = \frac{1}{-n+1}x^{-n+1} + \text{const}$

$\int \frac{1}{ax+b}\ dx = \frac{1}{a}\ln|ax+b| + \text{const}$

$\int e^x\ dx = e^x + \text{const}$

$\int a^x\ dx = \frac{a^x}{\\ln a} + \text{const}$

$\int \sin(x)\ dx = -\cos(x) + \text{const}$

$\int \cos(x)\ dx = \sin(x) + \text{const}$

$\int \tan(x)\ dx = \ln|sec(x)| + \text{const}$

$\int \cot(x)\ dx = \ln|\sin(x)| + \text{const}$

$\int \frac{1}{\sqrt{1-x^2}} \ dx = \arcsin(x) + \text{const}$

$\int -\frac{1}{\sqrt{1-x^2}} \ dx = \arccos(x) + \text{const}$

$\int \frac{1}{1+ x^2}\ dx = \arctan(x) + \text{const}$

$\int -\frac{1}{1+x^2}\ dx = \text{arccot}(x) + \text{const}$

##### Integration by Parts

$\int u\ dv = uv - \int v\ du$

$\int\limits_{a}^{b} u\ dv = uv |_a^b - \int v\ du$

##### Trigonometric Substitutions

$\sqrt{a^2 - b^2x^2}$ $\Rightarrow x=\frac{a}{b}\sin\theta$ and $\cos^2\theta = 1 - \sin^2\theta$

$\sqrt{a^2 + b^2x^2}$ $\Rightarrow x=\frac{a}{b}\tan\theta$ and $\sec^2\theta = 1 + \tan^2\theta$

$\sqrt{b^2x^2 - a^2}$ $\Rightarrow x=\frac{a}{b}\sec\theta$ and $\tan^2\theta = \sec^2\theta - 1$

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