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int(xe^x)/(1+x^2)dx |
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Answer» SOLUTION :`INT(xe^x)/(1+x^2)dx=inte^x{1/(1+x)-1/(1+x)^2}dx` [Integrating by parts taking `1/(1+x)` as FIRST and `e^x` as second FUNCTION.] =`1/(1+x).e^x-int(-1)/(1+x)^2e^xdx-inte^x.1/(1+x)^2dx+C` =`1/(1+x)e^x+inte^x/(1+x)^2dx-inte^x/(1+x)^2dx+C` =`e^x/(1+x)+C` |
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