Advertisements
Advertisements
प्रश्न
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Advertisements
उत्तर
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
संबंधित प्रश्न
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following function w.r.t. x:
x9.sec2(x10)
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 : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate: `int "e"^sqrt"x"` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int cos^7 x "d"x`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int 1/(sinx.cos^2x)dx` = ______.
`int secx/(secx - tanx)dx` equals ______.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
