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 :`intxlogxdx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`sin x/(1+ cos x)`
Write a value of
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
Evaluate: `int "e"^sqrt"x"` dx
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
Evaluate `int(3x^2 - 5)^2 "d"x`
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
`int 1/(sinx.cos^2x)dx` = ______.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Evaluate `int (1+x+x^2/(2!)) dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
