Integrals
About this tool:
You can use this tool to find the integral of a mathematical expression.
Click here to show/hide a table of integrals of common mathematical functions.
Integral of the product of a constant and a function
$$ \int c[f(x) \, dx] = c \int f(x) dx $$Integral of a constant
$$ \int k \, dx = kx + C $$Integral of the sum of two functions
$$ \int [f(x) + g(x)] \, dx = \int f(x) \, dx + \int f(x) \, dx $$Integral of power functions
$$ \int x^n \, dx = \frac{x^{n+1}}{n+1} + C $$ $$ \int \frac{1}{x} \, dx = \ln |x| + C $$Integral of exponential functions
$$ \int e^x \, dx = e^x + C $$ $$ \int b^x \, dx = \frac{b^x}{\ln b} + C $$Integrals of the trigonometric functions
$$ \int \sin x \, dx = - \cos x + C $$ $$ \int \cos x \, dx = \sin x + C $$ $$ \int \sec^2 x \, dx = \tan x + C $$ $$ \int \csc^2 x \, dx = - \cot x + C $$ $$ \int \sec x \, \tan x \, dx = \sec x + C $$ $$ \int \csc x \, \cot x \, dx = - \csc x + C $$ $$ \int \frac{1}{x^2 + 1} \, dx = \tan^{-1} x + C $$ $$ \int \frac{1}{\sqrt{1 - x^2}} \, dx = \sin^{-1} x + C $$ $$ \int \sinh x \, dx = - \cosh x + C $$ $$ \int \cosh x \, dx = - \sinh x + C $$The substitution rule
If \( u = g(x) \): $$ \int f(g(x))g'(x) \, dx = \int f(u) \, du $$How to use this tool:
Write the mathematical function whose integral you want to calculate in the textbox.
Write the variable with respect to which the integral will be calculated. Use either x, y, z or t only.
DO NOT include the \( \int {dx} \) symbols.
Click "Integrate!"
Examples of valid expressions:
To input \( x^3 + x^2 + x \) write x^3 + x^2 + x
To input \( \frac{1}{x} \) write 1/x
To input \( \ln(x) \) write ln(x)
To input \( \log_{10}(x) \) write log(x, 10)
To input \( e^x \) write exp(x) or e^(x)
To input \( \sin x \) write sin(x)
To input \( \sin^{-1}x \) write asin(x)
To input \( \sinh x \) write sinh(x)