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Question

Solve x4x41dx

A
x+16logx1x+112tan1+c
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B
x+14logx1x+112tan1+c
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C
=x+logx1x+112tan1+c
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D
=x+14logx1x+1+12tan1+c
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Solution

The correct option is B x+14logx1x+112tan1+c
x4x41dx
x41x41+1x41dx
dx+1x41dx
=x+1x41dx
=x+1(x21)(x2+1)dx
=x+121(x21)dx121(x2+1)dx [1x2a2dx=12alogxax+a+c]

=x+1212×1logx1x+112tan1x

=x+14logx1x+112tan1+c

Hence, the answer is x+14logx1x+112tan1+c.

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