Advertisements
Advertisements
Question
Integrate the functions:
`e^(2x+3)`
Advertisements
Solution
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
RELATED QUESTIONS
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
`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 : x3 + x2 – x + 1
Evaluate the following integrals : tan2x dx
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
`int sqrt(1 + sin2x) dx`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
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)`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int(5x + 2)/(3x - 4) dx` = ______
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
Write `int cotx 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 the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate `int 1/(x(x-1)) dx`
