Advertisements
Advertisements
प्रश्न
Integrate the functions:
`sin x/(1+ cos x)`
Advertisements
उत्तर
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
संबंधित प्रश्न
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of\[\int \log_e x\ dx\].
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals: `int sin 4x cos 3x dx`
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)`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int "x" * "e"^"2x"` dx
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int (7x + 9)^13 "d"x` ______ + c
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
If f'(x) = `x + 1/x`, then f(x) is ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate:
`int sqrt((a - x)/x) dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate `int1/(x(x-1))dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
