Integration by Parts Calculator

This does integration by parts for the cases that finish exactly: a polynomial multiplied by e^(kx), sin(kx), cos(kx) or ln(kx). Enter the polynomial, pick the second factor and its constant k, and you get the antiderivative, the choice of u and dv behind it and the whole D-I table row by row, with a definite value if you also give two limits. The polynomial is u for the first three, because differentiating it repeatedly reaches zero and that is what stops the table; for the logarithm it is the other way round, since ln has no elementary antiderivative but differentiates to 1/x. There is no computer algebra system behind this page, so anything outside that grammar is refused rather than guessed at, and so is a k small enough that the repeated division by it would lose the answer in rounding.