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Indefinite Integral Calculator

Find antiderivatives with full step-by-step working. Supports power rule, u-substitution, integration by parts, trig, exponential, logarithmic, and partial fractions — with verification by differentiation.

Power rule · u-sub · By parts · Trig · Exponential · Logarithmic · Verification

∫ f(x) dx

Enter the integrand — the function to be integrated

∫
dx
∫ f(x) dx
Quick Examples
Result Preview
∫ f(x) dx =
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Technique—
Function type—
Terms—
Integration Rules
∫ xⁿ dxxⁿ⁺¹/(n+1)
∫ 1/x dxln|x|
∫ eˣ dxeˣ
∫ aˣ dxaˣ/ln(a)
∫ sin x dx-cos x
∫ cos x dxsin x
∫ tan x dx-ln|cos x|
∫ sec²x dxtan x
∫ ln x dxx·ln x - x
∫ 1/(x²+1)arctan x
∫ 1/√(1-x²)arcsin x
Integration by Parts
∫ u dv = uv − ∫ v du
LIATE order for choosing u:
Log · Inverse trig · Algebraic · Trig · Exponential
u-Substitution
Look for a function and its derivative inside the integral. Set u = inner function.
∫ f(g(x))·g'(x) dx\n= ∫ f(u) du