Advertisements
Advertisements
प्रश्न
Integrate the functions:
`cos sqrt(x)/sqrtx`
Advertisements
उत्तर
Let I = `int (cos sqrtx)/sqrtx` dx
Put `sqrt x = t`
`1/(2 sqrt x)` dx = dt or `1/sqrt x` dx = 2 dt
Hence, `I = 2 int cos t dt`
`= 2 sin t + C = 2 sin sqrt x + C`
APPEARS IN
संबंधित प्रश्न
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Write a value of
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
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 integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate `int 1/(x (x - 1))` dx
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int log ("x"^2 + "x")` dx
`int (cos2x)/(sin^2x) "d"x`
`int x/(x + 2) "d"x`
`int(5x + 2)/(3x - 4) dx` = ______
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int (cos x)/(1 - sin x) "dx" =` ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) 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).
