Primitives table

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 integral is to use various transformations to convert the initial integral to the elementary one. Some of the elementary integrals are presented below.

1. Power function:

xadxxa1a1C
1xdxlnxC

2. Exponential and logarithmic functions:

axdxaxlnxC
exdxexC
logxadxxlnxxlnaC
lnxdxxlnxxC

3. Trigonometric functions:

sinxdxcosxC
cosxdxsinxC
tgxdxlncosxC
ctgxdxlnsinxC
1cos2xdxtgxC
1sin2xdxctgxC
1cosxdxlncosecxctgxC
1sinxdxlnsecxtgxC

4. Inverse trigonometric function:

arcsinxdxxarcsinx1x2C
arccosxdxxarccosx1x2C
arctgxdxxarctgx12ln1x2C
arcctgxdxxarcctgxln1x22C

5. Fractional rational function:

1a2x2dx1aarctgxaC
11x2dxarctgxC
1a2x2dx12alnaxaxC
11x2dx12ln1x1xC

Other useful links:

SLAE by inverse matrix method online calculator
Polynomial equations online calculator
Cubic equations online calculator

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