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Tools · Mathematics · Calculus

Integration Method Finder

Describe the shape of an integral. Get a ranked first move—and the reason it fits.

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Vocab
Integrand
Math glossaryIntegrand
∫f(x)⏟integrand dx\int \underbrace{f(x)}_{\text{integrand}}\,dx

The expression being integrated.

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Indefinite integral
Math glossaryIndefinite integral
∫f(x) dx=F(x)+C\int f(x)\,dx=F(x)+C

The family of all antiderivatives of an integrand.

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u-substitution
Math glossaryu-substitution
u=g(x),du=g′(x) dxu=g(x),\quad du=g'(x)\,dx

Reverses the chain rule by changing the integration variable.

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Integration by parts
Math glossaryIntegration by parts
∫u dv=uv−∫v du\int u\,dv=uv-\int v\,du

Reverses the product rule for integration.

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Partial fractions
Math glossaryPartial fractions
p(x)q(x)=∑ax−r\frac{p(x)}{q(x)}=\sum\frac{a}{x-r}

Decomposes a proper rational function into simpler rational terms.

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Math glossary