Integral Calculator
Mathematics Lab · Definite and indefinite integrals with worked steps
Syntax: x^2 (powers), sqrt(x) (roots), log(x) (logarithms), exp(x) (exponentials), sin(x), cos(x), atan(x). Use * for multiplication.
Examples: x^2*log(x), 3*x^2*exp(x^3+1), 2*x*cos(x^2), (x^2+1)/(x+1).
Result
Result checked by the calculator. For supported cases, the derivative of the antiderivative is also checked. The letter C denotes an arbitrary constant. The result holds on each interval where the function is defined.
Steps
- Power rule for integration: \(\displaystyle\int 3\cdot x^{2}\,dx = x^{3}\)
- Power rule for integration: \(\displaystyle\int 2\cdot x\,dx = x^{2}\)
- Integral of a constant: \(\displaystyle\int 1\,dx = x\)
How do I find an indefinite integral?
I look for an antiderivative whose derivative equals the input function. The result includes the arbitrary constant C.
The calculator applies exact rules to supported functions and displays the steps. Unsupported functions are reported rather than assigned an invented antiderivative.
Rules and examples
For powers, I use the rule \(\int x^n\,dx=\frac{x^{n+1}}{n+1}+C\) for \(n\neq-1\). For \(1/x\), I use \(\ln|x|+C\), on each interval of the domain.