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(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`1/(x-sqrtx)`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Write a value of
Write a value of
Write a value of
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals:
`int x/(x + 2).dx`
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : tan5x
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`
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int "e"^sqrt"x"` dx
`int 1/(xsin^2(logx)) "d"x`
`int x/(x + 2) "d"x`
`int cos^7 x "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int sin^-1 x`dx = ?
`int(5x + 2)/(3x - 4) dx` = ______
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Evaluate `int1/(x(x - 1))dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate:
`intsqrt(sec x/2 - 1)dx`
How should a substitution be chosen?
