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Question

If dxx+x7=p(x), then x6x+x7dx is equal to
(where C is constant of integration)

A
ln|x|p(x)+C
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B
ln|x|+p(x)+C
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C
xp(x)+C
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D
x+p(x)+C
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Solution

The correct option is A ln|x|p(x)+C
Let
I=x6x+x7dx
I=x6x(1+x6)dx
I=(1+x6)1x(1+x6)dx
I=1xdx1x+x7dx
I=ln|x|p(x)+C

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