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
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Write a value of
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following:
`int sinx/(sin 3x) dx`
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
Evaluate: `int "x" * "e"^"2x"` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int cos sqrtx` dx = _____________
`int sec^6 x tan x "d"x` = ______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
The value of `intsinx/(sinx - cosx)dx` equals ______.
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate `int 1/(x(x-1)) dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
Which expression results after simplifying \[\int\frac{\sin(t-a)}{\sin t}\,dt\]?
