Primitives table

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Integrals of the elementary functions and some little bit complex expressions often occur in practice are presented. The main idea behind the calculation of indefinite integrals is to use various transformations to convert the initial integral to the known one. Some of the known (simple) integrals are presented below.

1. Power function:

integral of the function x^a
integral of the function 1/x



2. Exponential and logarithmic functions:

integral of the function a^x

integral of the function log(x,a)

integral of the exponential function

integral of the natural logarithmic function





3. Trigonometric functions:

integral of the sine function

integral of the tangent function

integral of the function 1/cos(x)^2

integral of the function 1/cos(x)

integral of the cosine function

integral of the cotangent function

integral of the function 1/sin(x)^2

integral of the function 1/sin(x)












4. Inverse trigonometric function:

integral of the arcsine function

integral of the arctangent function

integral of the arccosine function

integral of the arccotangent function






5. Fractional rational function:

integral of the function 1/(a^2+x^2)

integral of the function 1/(a^2-x^2)

integral of the function 1/(1+x^2)

integral of the function 1/(1-x^2)