Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x.
`sqrt(x)(x^3 - 2x + 3)`
उत्तर
`sqrt(x)(x^3 - 2x + 3) = x^(1/2) (x^3 - 2x + 3)`
= `x^(7/2) - 2^(3/2) + 3x^(1/2)`
So `int sqrt(x)(x^3 - 2x + 3) "d"x = int x^(7/2) "d"x - int 2x^(3/2) "d"x + int 3x^(1/2) "d"x`
= `x^(7/2 + 1)/(7/2 + 1) - (2x^(3/2 + 1))/(3/2 + 1) + (3x^(1/2 + 1))/(1/2 + 1) + "c"`
= `2/9x^(9/2) - (2x^(5/2))/(5/2) + (3x^(3/2))/(3/2) + "c"`
= `2/9x^(9/2) - 4/5x^(5/2) + 2x^(3/2) + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the following with respect to x.
If f'(x) = x + b, f(1) = 5 and f(2) = 13, then find f(x)
Integrate the following with respect to x.
`(x^3 + 3x^2 - 7x + 11)/(x + 5)`
Integrate the following with respect to x.
`(3x^2 - 2x + 5)/((x - 1)(x^2 + 5))`
Integrate the following with respect to x.
x3e3x
Integrate the following with respect to x.
xn log x
Integrate the following with respect to x.
`1/(2x^2 - 9)`
Integrate the following with respect to x.
`"e"^x/("e"^(2x) - 9)`
Choose the correct alternative:
`int_0^(pi/3) tan x "d"x` is
Evaluate the following integral:
`int_0^3 (x dx)/(sqrt(x + 1)+ sqrt(5x + 1))`
Integrate the following with respect to x.
`sqrtx (x^3 - 2x + 3)`
