Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
उत्तर
Let I = `int sqrt(tanx)/(sin x . cosx).dx`
Dividing numerator and denominator by cos2x, we get
I = `int(((sqrttanx)/(cos^2x)))/((sinx/cosx)).dx`
= `int (sqrt(tanx).sec^2x)/tanx.dx`
= `int sec^2x/sqrt(tanx).dx`
Put tan x = t
∴ sec2xdx = dt
∴ I = `int (1)/sqrt(t)dt`
= `int t^(-1/2) dt`
= `t^(1/2)/(1/2) + c`
= `2sqrt(t) + c`
= `2sqrt(tanx) + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Integrate the functions:
cot x log sin x
Integrate the functions:
`(1+ log x)^2/x`
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals : `int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x:
`(10x^9 10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3)dx`
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
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 ("d"x)/(x(x^4 + 1))` = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int (f^'(x))/(f(x))dx` = ______ + c.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
Write `int cotx dx`.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
`int x^3 e^(x^2) dx`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate:
`intsqrt(sec x/2 - 1)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
