Table Of Indefinite Integrals Math

A couple of warnings are now in order. The indefinite integral is x 4 3 x 9 d x 1 5 x 5 3 2 x 2 9 x c x 4 3 x 9 d x 1 5 x 5 3 2 x 2 9 x c. Table of integrals basic forms z xndx 1 n 1 xn 1 1 z 1 x dx lnjxj 2 z udv uv z vdu 3 z 1 ax b dx 1 a lnjax bj 4 integrals of rational functions z 1 x a 2 dx ln 1 x a 5 z x a ndx x a n 1 n 1 n6 1 6 z x x a ndx x a n 1 n 1 x a n 1 n 2 7 z 1 1 x2 dx tan 1 x 8 z 1 a2 x2 dx 1 a tan 1 x a 9 z x a 2 x dx 1 2 lnja2 x2j 10 z x2 a 2 x dx x atan 1 x a 11 z x3 a 2 x.

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Since this is really asking for the most general anti derivative we just need to reuse the final answer from the first example.

Table of indefinite integrals math. More compact collections can be found in e g. In contrast to derivatives there are no ready made formulas that can calculate the integral of any function in routine way in general integration requires more sophisticated methods adapted to the specific problem. Brychkov marichev prudnikov s tables of indefinite integrals or as chapters in zwillinger s crc standard mathematical tables and formulae or bronshtein and semendyayev s guide book to mathematics handbook of mathematics or users guide to mathematics and other mathematical handbooks. Indefinite integrals step by step examples.

Add one to the exponent. Divide by the same. Basic integrals rational integrals trigonometric integrals 1 displaystyle int x n dx frac x n 1 n 1 c qquad n ne 1 2. A formula useful for solving indefinite integrals is that the integral of x to the nth power is one divided by n 1 times x to the n 1 power all plus a constant term.

Table shows indefinite integrals antiderivative of selected functions.