Advertisements
Advertisements
Question
Integrate the following with respect to x.
`(x^4 - x^2 + 2)/(x - 1)`
Solution
= `int(x^4 - x^2 + 2)/((x - 1)) "d"x`
= `int [(x^4 - xx^2)/((x - 1)) + 2/((x - 1))] "d"x`
= `int [(x^2(x^2 - 1))/((x - 1)) + 2/((x - 1))] "d"x`
= `int (x^2(x + 1)(x - 1))/((x - 1)) + 2/((x - 1))] "d"x`
= `int [(x^3 + x^2) + 2/((x - 1))] "d"x`
= `x^4/4 + x^3/3 + 2 log |x - 1| + "c"`
APPEARS IN
RELATED QUESTIONS
Integrate the following with respect to x.
If f'(x) = 8x3 – 2x and f(2) = 8, then find f(x)
Integrate the following with respect to x.
`(cos 2x + 2sin^2x)/(cos^2x)`
Integrate the following with respect to x.
`1/(sin^2x cos^2x) ["Hint:" sin^2x + cos^2x = 1]`
Integrate the following with respect to x.
x3e3x
Integrate the following with respect to x
`1/(x log x)`
Integrate the following with respect to x.
`"e"^x/("e"^(2x) - 9)`
Choose the correct alternative:
`int (2x + 3)/sqrt(x^2 + 3x + 2) "d"x` is
Choose the correct alternative:
`int_0^4 (sqrt(x) + 1/sqrt(x)) "d"x` is
Evaluate the following integral:
`int sqrt(2x^2 - 3) "d"x`
Evaluate the following integral:
`int (x + 1)^2 log x "d"x`
