Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x.
ex(1 + x) log(xex)
उत्तर
ex(1 + x) log(xex) = (ex + xex) log(xex)
Let z = xex
Then dz = d(xex)
dz = (xex + ex) dx .......(Using product rule)
So `int "e"^x (1 + x) log(x"e"^x) "d"x`
= `int log (x"e"^x) ("e"^x + x"e"^x) "d"x`
= `int log z "d"z`
= z(log z – 1) + c
= xex [log (xex) – 1] + c
APPEARS IN
संबंधित प्रश्न
Integrate the following with respect to x.
`(x^3 + 3x^2 - 7x + 11)/(x + 5)`
Integrate the following with respect to x.
`(4x^2 + 2x + 6)/((x + 1)^2(x - 3))`
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.
xn log x
Integrate the following with respect to x.
`"e"^(2x)/("e"^(2x) - 2)`
Integrate the following with respect to x.
`1/sqrt(x^2 - 3x + 2)`
Choose the correct alternative:
`int (sin5x - sinx)/(cos3x) "d"x` is
Choose the correct alternative:
`int logx/x "d"x, x > 0` is
Evaluate the following integral:
`int (x + 1)^2 log x "d"x`
