Advertisements
Advertisements
प्रश्न
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Advertisements
उत्तर
Let I = `int (2 cos x - 3 sin x)/(6 cos x + 4 sin x)` dx
`= 1/2 int (2 cos x - 3 sin x)/(3 cos x + 2 sin x)` dx
Put 3 cos x + 2 sin x = t
(- 3 sin x + 2 cos x) dx = dt
Hence, `I = 1/2 int 1/t` dt
`= 1/2 log abs t + C`
`= 1/2 log abs (3 cos x + 2 sin x) + C`
APPEARS IN
संबंधित प्रश्न
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
cot x log sin x
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Write a value of
Write a value of
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x : tan5x
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
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 (5"x" + 1)^(4/9)` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int cos sqrtx` dx = _____________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
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 ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
