Choose the correct answer
`intsqrt(x^2-8x+7)dx`

Options

A. `1/2(x-4)sqrt(x^2-8x+7)+9log|x-4+sqrt(x^2-8x+7)|+C`
B. `1/2(x+4)sqrt(x^2-8x+7)+9log|x+4+sqrt(x^2-8x+7)|+C`
C. `1/2(x-4)sqrt(x^2-8x+7)-3sqrt(2)log|x-4+sqrt(x^2-8x+7)|+C`
D. `1/2(x-4)sqrt(x^2-8x+7)-(9/2)log|x-4+sqrt(x^2-8x+7)|+C`

Answer

D

Explanation

`I=int(sqrt(x^2-8x+7))dx`

`I=int(sqrt((x-4)^2-3^2))dx`

We know that

`int(sqrt(x^2-a^2))=x/2sqrt(x^2-a^2)-a^2/2log|x+sqrt(x^2-a^2)|+C`


Put a=3 and x=x-4

We have

`I=(x-4)/2sqrt(x^2-8x+7)+1/2log|x-4+sqrt(x^2-8x+7)|+C`

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