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
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
cot x log sin x
Integrate the functions:
`1/(1 + cot x)`
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate `int (3"x"^2 - 5)^2` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Evaluate `int (5"x" + 1)^(4/9)` dx
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int sec^6 x tan x "d"x` = ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
