Advertisements
Advertisements
प्रश्न
Evaluate : `∫1/(3+2sinx+cosx)dx`
Advertisements
उत्तर
let I=`∫1/(3+2sinx+cosx)dx`
put `tan(x/2)=t`
`x=2tan^-1t`
`dx=(2dt)/(1+t^2)` and `sinx=2t/(1+t^2), cosx((1-t^2)/(1+t^2))`
`therefore I=tan^-1[tan(x/2)+1]+c`
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
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 w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `int sin x/cos^2x dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
`int sqrt(1 + "x"^2) "dx"` =
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate `int 1/((2"x" + 3))` dx
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Write `int cotx dx`.
Find `int dx/sqrt(sin^3x cos(x - α))`.
`int secx/(secx - tanx)dx` equals ______.
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate the following
`int1/(x^2 +4x-5)dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
