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 : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
sec2(7 – 4x)
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of
Write a value of
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Evaluate the following integrals:
tan2x dx
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int cos sqrtx` dx = _____________
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int dx/(1 + e^-x)` = ______
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
Write `int cotx dx`.
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
