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B
x33tan−1x+16x2+16log(x2+1).
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C
x33tan−1x−13x2+16log(x2+1).
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D
x33tan−1x−16x2+13log(x2+1).
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Solution
The correct option is Ax33tan−1x−16x2+16log(x2+1). Integrating by parts, I=x33tan−1x−13∫x3x2+1dx. =x33tan−1x−13∫(x−xx2+1)dx =x33tan−1x−16x2+16log(x2+1)+c.