Advertisements
Advertisements
प्रश्न
Integrate the functions:
`x/(e^(x^2))`
Advertisements
उत्तर
Let `I = int x/ (e^(x^(2))) dx`
Put x2 = t
⇒ 2x dx = dt
∴ `I = 1/2 int dt/e^t`
`= 1/2 int e^-t dt`
`= 1/2 (e^-t/-1) + C`
`= -1/(2e^t) + C`
`= -1/ 2^(e^(x^2)) + C`
APPEARS IN
संबंधित प्रश्न
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
cot x log sin x
Integrate the functions:
`1/(1 + cot x)`
Evaluate: `int 1/(x(x-1)) dx`
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
Evaluate: `int "e"^sqrt"x"` dx
`int(log(logx))/x "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int ("d"x)/(x(x^4 + 1))` = ______.
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate `int 1/(x(x-1)) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
