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
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate: `int 1/(x(x-1)) dx`
`int "dx"/(9"x"^2 + 1)= ______. `
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int 1/(4"x"^2 - 20"x" + 17)` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
Evaluate: `int "e"^sqrt"x"` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int cot^2x "d"x`
`int(1 - x)^(-2) dx` = ______.
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
