Advertisements
Advertisements
प्रश्न
`int x^3"e"^(x^2) "d"x`
Advertisements
उत्तर
Let I = `int x^3*"e"^(x^2) "d"x`
= `int x^2*x"e"^(x^2) "d"x`
Put x2 = t
∴ 2x.dx = dt
∴ x dx = `"dt"/2`
∴ I = `1/2 int"te"^"t" "dt"`
= `1/2 ["t" int"e"^"t" "dt" - int["d"/"dt"("t") int"e"^"t""dt"]"dt"]`
= `1/2 ["te"^"t" - int1*"e"^"t""dt"]`
= `1/2 ("te"^"t" - "e"^"t") + "c"`
= `1/2 "e"^"t" ("t" - 1) + "c"`
∴ I = `1/2 "e"^(x^2) (x^2 - 1) + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`(2x)/(1 + x^2)`
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
If f'(x) = `x + 1/x`, then f(x) is ______.
`int x^3 e^(x^2) dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate:
`int sqrt((a - x)/x) dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
