Advertisements
Advertisements
प्रश्न
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Advertisements
उत्तर
Let `I = int (sin x)/(1 + cos x)^2` dx
Put 1 + cos x = t
⇒ - sin x dx = dt
∴ `I = - int dt/t^2 = t^(-2 + 1)/(-2 + 1) + C`
`= 1/t + C`
`= 1/(1 + cos x) + C`
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Integrate the functions:
`(1+ log x)^2/x`
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
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:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int(log(logx))/x "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int dx/(1 + e^-x)` = ______
`int (cos x)/(1 - sin x) "dx" =` ______.
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int ("d"x)/(x(x^4 + 1))` = ______.
Write `int cotx dx`.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
`int secx/(secx - tanx)dx` equals ______.
Evaluate `int (1+x+x^2/(2!))dx`
Evaluate:
`int sin^2(x/2)dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
