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B
xlog(1+x2)−2x+2tan−1x.
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C
xlog(1+x2)+2x+2tan−1x.
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D
xlog(1−x2)−2x+2tan−1x.
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Solution
The correct option is Bxlog(1+x2)−2x+2tan−1x. I=∫log(1+x2)dx=∫1.log(1+x2)dx xlog(1+x2)−∫x.11+x2.2xdx xlog(1+x2)−2∫x2+1−1x2+1dx =xlog(1+x2)−2∫[1−11+x2]dx =xlog(1+x2)−2x+2tan−1x.