Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Advertisements
उत्तर
Let I = `int(x^n - 1)/sqrt(1 + 4x^n).dx`
Put xn = t
∴ nxn–1 dx = dt
∴ xn–1 dx = `dt/n`
∴ I = `int (1)/sqrt(1 + 4t).dt/n`
= `(1)/nint(1 + 4t)^(-1/2)dt`
= `1/n.((1 + 4t)^(1/2))/(1/2) xx (1)/(4) + c`
= `(1)/(2n).sqrt(1 + 4x^n) + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`x/(e^(x^2))`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Evaluate the following integrals: `int sin 4x cos 3x dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate `int 1/(x (x - 1))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int cos sqrtx` dx = _____________
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int (f^'(x))/(f(x))dx` = ______ + c.
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "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).
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
Which standard substitution is used for \[\sqrt{x^2+\mathrm{a}^2}\], \[\frac{1}{\sqrt{x^2+\mathrm{a}^2}}\], or \[x^2+\mathrm{a}^2\]?
After choosing \[u=g(x)\], what is the next step?
What is \[\int\frac{\sin x}{\sin(x+a)}\,dx\]?
