Advertisements
Advertisements
प्रश्न
`int x^3"e"^(x^2) "d"x`
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:
`1/(1 + cot x)`
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Evaluate: ∫ |x| dx if x < 0
Choose the correct alternative:
`int(1 - x)^(-2) dx` = ______.
The value of `intsinx/(sinx - cosx)dx` equals ______.
Write `int cotx dx`.
Evaluate `int1/(x(x - 1))dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
