let u = x du=dx
let dv= e^x v=e^x
∫ xe^(x)dx =
xe^x - ∫ e^(x)dx
= xe^x - e^x
= e^x ( x-1 ) + c
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An indefinite integral is a version of an integral that, unlike a definite integral, returns an expression instead of a number. The general form of a definite integral is: ∫ba f(x) dx. The general form of an indefinite integral is: ∫ f(x) dx. An example of a definite integral is: ∫20 x2 dx. An example of an indefinite integral is: ∫ x2 dx In the definite case, the answer is 23/3 - 03/3 = 8/3. In the indefinite case, the answer is x3/3 + C, where C is an arbitrary constant.
∫ cos(x) dx = -sin(x) + C
By antiderivative do you mean integral? If yes, integral x^1 dx= (x^2)/2
integral x/(x-1) .dx = x - ln(x-1) + c where ln = natural logarithm and c = constant of integration alternatively if you meant: integral x/x - 1 .dx = c
∫ af(x) dx = a ∫ f(x) dx