Advertisements
Advertisements
प्रश्न
Evaluate `int (1 + x + x^2/(2!))`dx
Advertisements
उत्तर
`int (1 + x + x^2/(2!))`dx
`= int 1 dx + int x dx + 1/(2!) int x^2 dx`
`= x + x^2/2 + 1/(2!) xx x^3/3 + c`
∴ `x + x^2/2 + x^3/6 + c`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
`int "dx"/(9"x"^2 + 1)= ______. `
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : cos7x
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Write `int cotx dx`.
`int secx/(secx - tanx)dx` equals ______.
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
