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
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
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 : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
Evaluate: ∫ |x| dx if x < 0
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int sqrt(1 + sin2x) dx`
`int logx/x "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int (f^'(x))/(f(x))dx` = ______ + c.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
