Advertisements
Advertisements
Question
Integrate the functions:
`sin x/(1+ cos x)`
Advertisements
Solution
Let `I = int (sin x)/(1 + cos x) dx`
Put 1 + cos x = t
⇒ -sin x dx = dt
∴ `I = - int dt/t = -log |t| + C `
= - log |1 + cos x| + C
`= log (1/ (|1 + cos x|)) + C`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t.x:
cos8xcotx
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
`int sqrt(1 + sin2x) dx`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate:
`int sin^3x cos^3x dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
