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21 Σεπ 2016 · What is the antiderivative of x ln x? ∫xlnxdx = x2 4 (2lnx − 1) +C, or, x2 4 ln(x2 e) +C, or ln(x2 e)x2 4 +C. Let I = ∫xlnxdx. We use the following Rule of Integration by Parts (IBP) : ∫uvdx = u∫vdx − ∫[du dx ∫vdx]dx. We take, u = lnx ⇒ du dx = 1 x, and,v = x ⇒ ∫vdx = ∫xdx = x2 2. Hence, I = x2 2 lnx −∫[1 x ⋅ x2 2]dx. = x2 2 lnx − 1 2∫xdx.
Antiderivative calculator finds the antiderivative of a function step by step with respect to a variable i.e., x, y, or z. This online integration calculator also supports upper bound and lower bound in case you are working with minimum or maximum value of intervals.
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The Integral Calculator lets you calculate integrals and antiderivatives of functions online — for free! Our calculator allows you to check your solutions to calculus exercises. It helps you practice by showing you the full working (step by step integration).
23 Νοε 2016 · What is the antiderivative of (x ln x − x)? This is the same as asking. ∫(xlnx − x)dx. Splitting up the integral: = ∫xlnxdx − ∫xdx. The second can be integrated using the power rule for integration: = ∫xlnxdx − x2 2. For the remaining integral, use integration by parts. This takes the form ∫udv = uv − ∫vdu. For ∫xlnxdx, let:
