Advertisements
Advertisements
प्रश्न
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
Advertisements
उत्तर
Let I = `int"e"^x (1/x - 1/x^2) "d"x`
Put f(x) = `1/x`
∴ f'(x) = `-1/x^2`
∴ I = `int"e"^x ["f"(x) + "f'"(x)] "d"x`
= `"e"^x*"f"(x) + "c"`
∴ I = `"e"^x* 1/x + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`sin x/(1+ cos x)`
Write a value of
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Evaluate: `int 1/(sqrt("x") + "x")` dx
`int(log(logx))/x "d"x`
`int x^3"e"^(x^2) "d"x`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int dx/(1 + e^-x)` = ______
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate `int 1/("x"("x" - 1)) "dx"`
`int x^3 e^(x^2) dx`
Evaluate:
`int sin^2(x/2)dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate:
`intsqrt(sec x/2 - 1)dx`
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
For \[\sqrt{\frac{x-\alpha}{\beta-x}}\] or \[\sqrt{(x-\alpha)(\beta-x)}\], where \[\beta>\alpha\], which substitution is used?
When applying substitution, what must always be rewritten in terms of the new variable?
