Calculus visual reference

Common Integrals Chart

An indefinite integral describes a family of antiderivatives. Match the integrand to a known derivative pattern, reverse that derivative, and include the constant of integration.

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Common integrals chart showing power reciprocal exponential basic trigonometric constant multiple and sum difference antiderivative rules with plus C
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How to read it

Use the chart as a decision tool.

A printable common integrals chart focused on Calculus I antiderivatives, including the power rule, 1/x, eˣ, basic trig integrals, constant multiples, sums, and +C. Read the label first, identify the matching structure in your problem, then confirm that any stated conditions apply before substituting values.

01

Algebraic and exponential

These are the most common Calculus I patterns.

Power rule

∫xn dx=xn+1n+1+C\displaystyle \int x^n\,dx=\frac{x^{n+1}}{n+1}+C

Reciprocal

∫1x dx=ln⁡∣x∣+C\displaystyle \int\frac1x\,dx=\ln|x|+C

Natural exponential

∫ex dx=ex+C\displaystyle \int e^x\,dx=e^x+C

Constant multiple

∫cf(x) dx=c∫f(x) dx\displaystyle \int cf(x)\,dx=c\int f(x)\,dx

Sum / difference

∫(f±g) dx=∫f dx±∫g dx\displaystyle \int(f\pm g)\,dx=\int f\,dx\pm\int g\,dx
02

Basic trigonometric

Read each as the reverse of a derivative rule.

Cosine

∫cos⁡x dx=sin⁡x+C\displaystyle \int\cos x\,dx=\sin x+C

Sine

∫sin⁡x dx=−cos⁡x+C\displaystyle \int\sin x\,dx=-\cos x+C

Secant squared

∫sec⁡2x dx=tan⁡x+C\displaystyle \int\sec^2x\,dx=\tan x+C

Cosecant squared

∫csc⁡2x dx=−cot⁡x+C\displaystyle \int\csc^2x\,dx=-\cot x+C
How to remember it

Differentiate your answer to check it

  1. 1For powers, add one to the exponent and divide by the new exponent.
  2. 2The power rule excludes n=−1; 1/x integrates to ln|x|.
  3. 3Every indefinite integral needs +C.
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