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Question

tan-13x-x31-3x2 dx

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Solution

Let I= tan-1 3x-x31-3x2 dx=3 tan-1 x dx=3tan-1 x×1 dx=3 tan-1 x×x-11+x2×x dx=3x tan-1 x-3x1+x2 dxlet 1+x2=t2x dx=dtThen,I=3x tan-1x-32dtt=3x tan-1x-32 log t+C=3x tan-1x-32 log 1+x2+C

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