Advertisements
Advertisements
प्रश्न
Evaluate `int x log x "d"x`
उत्तर
Let I = `int x* log x "d"x`
= `log x int x"d"x - int["d"/("d"x) (log x) int x"d"x] "d"x`
= `log x* x^2/2 - int[1/x xx x^2/2] "d"x`
= `x^2/2 log x - 1/2 int x "d"x`
= `x^2/2 log x - 1/2* x^2/2 + "c"`
∴ I = `x^2/2 log x - x^2/4 + "c"`
APPEARS IN
संबंधित प्रश्न
Find : `int x^2/(x^4+x^2-2) dx`
Find: `I=intdx/(sinx+sin2x)`
Integrate the rational function:
`(2x - 3)/((x^2 -1)(2x + 3))`
Integrate the rational function:
`(x^3 + x + 1)/(x^2 -1)`
`int (xdx)/((x - 1)(x - 2))` equals:
Find `int (2cos x)/((1-sinx)(1+sin^2 x)) dx`
Integrate the following w.r.t. x: `(x^2 + 3)/((x^2 - 1)(x^2 - 2)`
Integrate the following with respect to the respective variable : `cot^-1 ((1 + sinx)/cosx)`
Evaluate: `int ("x"^2 + "x" - 1)/("x"^2 + "x" - 6)` dx
`int sqrt(4^x(4^x + 4)) "d"x`
`int 1/(sinx(3 + 2cosx)) "d"x`
State whether the following statement is True or False:
For `int (x - 1)/(x + 1)^3 "e"^x"d"x` = ex f(x) + c, f(x) = (x + 1)2
Evaluate `int x^2"e"^(4x) "d"x`
`int 1/(4x^2 - 20x + 17) "d"x`
Verify the following using the concept of integration as an antiderivative
`int (x^3"d"x)/(x + 1) = x - x^2/2 + x^3/3 - log|x + 1| + "C"`
Evaluate the following:
`int "e"^(-3x) cos^3x "d"x`
`int 1/(x^2 + 1)^2 dx` = ______.
Evaluate.
`int (5x^2 - 6x + 3) / (2x -3) dx`
