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Integrate (x^(2))/((a + bx)^(2))....

Integrate `(x^(2))/((a + bx)^(2))`.

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(b^(3))(a+bx-2a "log"(a+bx)-(a^(2))/(a+bx)+c)`
Let `I=(x^(2))/((a+bx)^(2))`
Put `a+bx=t rArr "b dx" =dt`
`therefore I=int((t-a)/(b))^(2)/t^(2)*(dt)/(b)=(1)/(b^(3))int((t^(2)-2 at + a^(2))/(t^(2)))dt`
`=(1)/(b^(3))int(1-(2a)/(t)+(a^(2))/(t^(2)))dt`
`(1)/(b^(3))(t-2 "a log t"-(a^(2))/(t))+c`
`=(1)/(b^(3))(a+bx-2 "a log"(a+bx)-(a^(2))/(a+bx)+c)`
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