Advertisements
Advertisements
प्रश्न
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
उत्तर
Let I = `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
`= -2 int 1/(sqrt("5x" - 4) - sqrt("5x" - 2)) xx (sqrt("5x" - 4) + sqrt("5x" - 2))/(sqrt("5x" - 4) + sqrt("5x" - 2))`dx
`= - 2 int (sqrt("5x" - 4) + sqrt("5x" - 2))/(("5x" - 4) - ("5x" - 2))` dx
`= -2 int (sqrt("5x" - 4) + sqrt("5x" - 2))/-2` dx
`= int [("5x" - 4)^(1/2) + ("5x" - 2)^(1/2)]`dx
`= int ("5x" - 4)^(1/2) "dx" + int ("5x" - 2)^(1/2)` dx
`= ("5x" - 4)^(3/2)/(3/2) xx 1/5 + ("5x" - 2)^(3/2)/(3/2) xx 1/5` + c
∴ I = `2/15 [("5x" - 4)^(3/2) + ("5x" - 2)^(3/2)]` + c
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`sqrt(sin 2x) cos 2x`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Evaluate the following integrals : `int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` 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
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
