how do you integrate x tan-1x dx, i know it can be done by integration by parts maybe, but i'm not sure.... i'm a student studying for a test.


Integration by parts is the way to solve this problem. I let u = tan-1x and dv = x dx which leads to

You should check your answer by differentiating or you can try The Integrator. The input is x*ArcTan[x], the capital letters and square brackets are required. (The arctangent or inverse tangent is written tan-1 rather than arctan in many textbooks.)

Claude and Harley
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