What Is the Integral of Xln(x)?


Quick Answer

The integral of xln(x) is x squared, times half the ln of x, minus x squared over four, plus a constant. In mathematical notation, the formula looks like the integral of xln(x) dx = x^2(ln(x)/2) - ((x^2)/4) + C, where C equals a constant.

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Full Answer

The equation for the integral xln(x) can be found through the integration techniques known as "integration by parts" and "the product rule." Following these rules, the two components of the equation x and ln(x) are separated out and expressed as d(fg) over dx. The integral function is also called the antiderivative because it works in the reverse of the derivative function.

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