Advertisements
Advertisements
प्रश्न
Write a value of\[\int a^x e^x \text{ dx }\]
Advertisements
उत्तर
∫ ax . ex dx
= ∫ (ae)x dx
APPEARS IN
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals: `int sin 4x cos 3x dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x : tan5x
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
`int 1/(xsin^2(logx)) "d"x`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate `int (1+x+x^2/(2!))dx`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
