Advertisements
Advertisements
प्रश्न
Integrate the functions:
`e^(2x+3)`
Advertisements
उत्तर
Let `I = int e^(2x + 3)` dx
Put 2x + 3 = t
2 dx = dt or dx = `1/2` dt
Hence, `I = 1/2 int e^t` dt
`= 1/2 e^t+ C`
`= 1/2 e^(2x + 3) + C`
APPEARS IN
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Integrate the functions:
`x/(e^(x^2))`
Write a value of
Write a value of
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
`int "dx"/(9"x"^2 + 1)= ______. `
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals:
`int x/(x + 2).dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Evaluate `int 1/((2"x" + 3))` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int x^3"e"^(x^2) "d"x`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int sec^6 x tan x "d"x` = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate:
`int sin^3x cos^3x dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate `int1/(x(x-1))dx`
