Advertisements
Advertisements
Question
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Advertisements
Solution
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
RELATED QUESTIONS
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
sin x ⋅ sin (cos x)
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate: `int "x" * "e"^"2x"` dx
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int logx/x "d"x`
`int cos^7 x "d"x`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int sin^-1 x`dx = ?
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int dx/(1 + e^-x)` = ______
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
