Advertisements
Advertisements
Question
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
Options
`1/2 log [(2x - 1) + sqrt(x^2 - x - 6)] + "c"`
tan−1 (2x − 1) + c
`log [(x - 1/2) + sqrt(x^2 - x - 6)] + "c"`
`log [(x - 1/2) + sqrt(x^2 + x + 6)] + "c"`
Advertisements
Solution
`int 1/sqrt((x - 3)(x + 2))` dx = `bbunderline(log [(x - 1/2) + sqrt(x^2 - x - 6)] + "c")`.
Explanation:
`int 1/sqrt((x - 3)(x + 2))` dx = `int 1/sqrt(x^2 - x - 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
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of
Write a value of
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int cot^2x "d"x`
`int(1 - x)^(-2) dx` = ______.
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
`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:
`int(sqrt(tanx) + sqrt(cotx))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^2 / (2!))dx`
After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?
