Advertisements
Advertisements
प्रश्न
`int (cos2x)/(sin^2x) "d"x`
Advertisements
उत्तर
`int (cos2x)/(sin^2x) "d"x`
= `int (1 - 2sin^2x)/(sin^2x) "d"x` ......[∵ cos 2θ = 1 − 2sin2θ]
= `int(1/(sin^2x) - (2sin^2x)/(sin^2x)) "d"x`
= `int ("cosec"^2x - 2) "d"x`
= −cot x − 2x + c
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`1/(1 - tan x)`
Evaluate: `int 1/(x(x-1)) dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : cos7x
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int1/(4 + 3cos^2x)dx` = ______
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
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` = ______.
`int 1/(sinx.cos^2x)dx` = ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Evaluate `int (1+x+x^2/(2!))dx`
Evaluate `int(1 + x + x^2/(2!))dx`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
