Explanation
∫((1+x2−1)tan−1x1+x2)dx=∫(1−(11+x2))tan−1xdx=∫1.tan−1dx−∫(tan−1x1+x2)dxUseILATEinfirstpartandassumetan−1x=tforsecondintegration=xtan−1x−∫(11+x2)×xdx−∫tdt=xtan−1x−(12)log|1+x2|−(t22)+C=xtan−1x−(12)log|1+x2|−((tan−1x)22)+C∴C=−(12)(tan−1x)2
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