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`
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: `int "e"^sqrt"x"` dx
`int(1 - x)^(-2) dx` = ______.
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
`int ("d"x)/(x(x^4 + 1))` = ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate the following.
`int x sqrt(1 + x^2) dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate:
`int sin^3x cos^3x dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
Which substitution is appropriate for \[\sqrt{\frac{x}{a-x}}\], \[\sqrt{\frac{a-x}{x}}\], \[\sqrt{x(a-x)}\], or \[\frac{1}{\sqrt{x(a-x)}}\]?
