Advertisements
Advertisements
Question
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Advertisements
Solution
Let `I = int (sqrt tan x)/(sinx cos x)` dx
`= int sqrt tan x/(sin x/ cos x * cos ^2) dx`
`= int sqrt tanx/tan x * sec^2 x dx`
`I = int (tan x)^((-1)/2)* sec^2 x dx`
Put tan x = t
sec2 x dx = dt
Hence, `I = int t^((-1)/2)dt = (t ^(1/2 + 1))/(1/2 + 1) + C`
`= 2 t^(1/2) + C`
`= 2 sqrt(tan x) + C`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate :`intxlogxdx`
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the functions:
cot x log sin x
Integrate the functions:
`1/(1 - tan x)`
Write a value of
Write a value of
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
`int "dx"/(9"x"^2 + 1)= ______. `
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate `int 1/(x (x - 1))` dx
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate:
`int sin^2(x/2)dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate `int 1/(x(x-1))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
