`intlog (1+x^(2))dx.`

1.	`intlog (1+x^(2))dx.`
Answer» Integrating by parts, taking log `(1+x^(2))` as the first function and 1 as the second function, we get `intlog(1+x^(2))dx=int{log(1+x^(2))1}dx` `=log(1+x^(2))intdx-int[(d)/(dx){log(1+x^(2))}int1dx]dx` `=log(1+x^(2))x-int(2x)/((1+x^(2)))*xdx` `=xlog(1+x^(2))-2int(x^(2))/((1+x^(2)))dx` `=log(1+x^(2))-2int(1-(1)/(1+x^(2)))dx` `=xlog(1+x^(2))-2intdx+2int(dx)/((1+x^(2)))` `=xlog(1+x^(2))-2x+2tan^(-1)x+C`.

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