Advertisements
Advertisements
प्रश्न
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Advertisements
उत्तर
Let I = `int 1/(3+2sinx + cosx) dx`
Put tan `x/2 = t` Then `dx = 2/(1+ t^2) dt`
`sinx = (2t)/(1+t^2) and cos x = (1- t^2)/(1+ t^2)`
`:. I = int (2dt"/" (1+t^2))/(3+2 ((2t)/(1+t^2))+((1-t^2)/(1+t^2)))`
`= 2int (dt"/"(1+t^2))/((3(1+t^2) + 4t + (1-t^2))/(1+t^2))`
= `2int (dt)/(2t^2 + 4t + 4) = int (dt)/((t+1)^2 + 1)`
`= tan^(-1) (t + 1) + c`
`= tan^(-1)[tan (x/2) + 1)] + c`
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
cot x log sin x
Write a value of
Write a value of
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Evaluate `int 1/((2"x" + 3))` dx
`int (sin4x)/(cos 2x) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int(1 - x)^(-2) dx` = ______.
`int(5x + 2)/(3x - 4) dx` = ______
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
`int 1/(sinx.cos^2x)dx` = ______.
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
Evaluate:
`intsqrt(sec x/2 - 1)dx`
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
