Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x.
`x^3/(x + 2)`
उत्तर
= `int x^3/((x + 2)) "d"x`
= `int (x^3 + 8 - 8)/((x + 2)) "d"x`
= `int ((x^3 + 2^3)/((x + 2)) - 8/((x + 2))) "d"x`
= `int [((x + 2)(x^2 - 2x + 4))/((x + 2)) - 8/((x + 2))] "d"x`
= `(xx^3/3 - (2x^2)/2 + x) - 8 log |x + 2| + "c"`
= `x^3/3 - x^2 + 4x - 8 log |x + 2| + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the following with respect to x.
`(3x^2 - 2x + 5)/((x - 1)(x^2 + 5))`
Integrate the following with respect to x.
x log x
Integrate the following with respect to x.
`(2x + 5)/(x^2 + 5x - 7)`
Integrate the following with respect to x.
x8(1 + x9)5
Integrate the following with respect to x.
`"e"^x [(x - 1)/(x + 1)^3]`
Choose the correct alternative:
`int 1/x^3 "d"x` is
Choose the correct alternative:
`int 2^x "d"x` is
Choose the correct alternative:
`int sqrt("e"^x) "d"x` is
Choose the correct alternative:
`int_0^4 (sqrt(x) + 1/sqrt(x)) "d"x` is
Evaluate the following integral:
`int ("d"x)/(2 - 3x - 2x^2)`
