Advertisements
Advertisements
Question
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Advertisements
Solution
Let I = `int 1/sqrt((x - 3)(x + 2)).dx`
= `int 1/sqrt(x^2 - x - 6).dx`
= `int 1/sqrt((x^2 - x + 1/4) - 1/4 - 6).dx`
= `int 1/sqrt((x - 1/2)^2 - (5/2)^2).dx`
= `log|(x - 1/2) + sqrt((x - 1/2)^2 - (5/2)^2)| + c`
= `log|(x - 1/2) + sqrt(x^2 - x - 6)| + c`.
APPEARS IN
RELATED QUESTIONS
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Integrate the functions:
`1/(1 + cot x)`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
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\[\int e^{ax} \sin\ bx\ dx\]
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int sqrt(1 + sin2x) dx`
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
If f'(x) = `x + 1/x`, then f(x) is ______.
`int (f^'(x))/(f(x))dx` = ______ + c.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
Evaluate the following.
`int1/(x^2+4x-5) dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate `int (1 + x + x^2/(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.
`intx^3/sqrt(1 + x^4)dx`
Evaluate `int1/(x(x - 1))dx`
