Advertisements
Advertisements
Question
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
Advertisements
Solution
Let I = `int ("e"^(3x))/("e"^(3x) + 1) "d"x`
Put e3x + 1 = t
Differentiating w.r.t. x, we get
3e3xdx = dt
∴ e3xdx = `"dt"/3`
∴ I = `int 1/"t"* "dt"/3 = 1/3 log |"t"| + "c"`
∴ I `1/3 log|"e"^(3x) + 1| + "c"`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
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`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Write a value of
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
Evaluate `int 1/((2"x" + 3))` dx
`int logx/x "d"x`
`int 1/(xsin^2(logx)) "d"x`
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int(log(logx) + 1/(logx)^2)dx` = ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
