Advertisements
Advertisements
प्रश्न
Evaluate `int(3x^2 - 5)^2 "d"x`
Advertisements
उत्तर
Let I = `int(3x^2 - 5)^2 "d"x`
= `int (9x^4 - 30x^2 + 25) "d"x`
= `9intx^4"d"x - 30int x^2"d"x + 25int"d"x`
= `9((x^5)/5) - 30((x^3)/3) + 25x + "c"`
∴ I = `9/5 x^5 - 10x^3 + 25x + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
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 : `(4e^x - 25)/(2e^x - 5)`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate `int 1/((2"x" + 3))` dx
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int (1 + x)/(x + "e"^(-x)) "d"x`
If f'(x) = `x + 1/x`, then f(x) is ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
`int 1/(sinx.cos^2x)dx` = ______.
Write `int cotx dx`.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate:
`int sqrt((a - x)/x) 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).
