Advertisements
Advertisements
Question
Integrate the functions:
`cos sqrt(x)/sqrtx`
Advertisements
Solution
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
RELATED QUESTIONS
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
cot x log sin x
Integrate the functions:
`1/(1 - tan x)`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of\[\int a^x e^x \text{ dx }\]
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).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 :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
`int cos sqrtx` dx = _____________
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)`
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int x^3"e"^(x^2) "d"x`
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
