Advertisements
Advertisements
Question
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Advertisements
Solution
Let I = `int 1/(sqrt(3"x"^2 - 5))` dx
`= 1/sqrt3 int 1/sqrt("x"^2 - 5/3)` dx
`= 1/sqrt3 int 1/(sqrt ("x"^2 - (sqrt5/sqrt3)^2))` dx
`= 1/sqrt3 log |"x" + sqrt("x"^2 - (sqrt5/sqrt3)^2)| + "c"_1`
`= 1/sqrt3 log |"x" + sqrt("x"^2 - 5/3)| + "c"_1`
`= 1/sqrt3 log |(sqrt3"x" + sqrt(3"x"^2 - 5))/sqrt3| + "c"_1`
`= 1/sqrt3 log |sqrt3"x" + sqrt(3"x"^2 - 5)| - 1/sqrt3 log sqrt3 + "c"_1`
∴ I = `1/sqrt3 log |sqrt3"x" + sqrt(3"x"^2 - 5)| + "c"`,
where c = `"c"_1 - 1/sqrt3 log sqrt3`
Notes
The answer in the textbook is incorrect.
APPEARS IN
RELATED QUESTIONS
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Write a value of
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : tan5x
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
`int cos sqrtx` dx = _____________
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int (sin4x)/(cos 2x) "d"x`
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int(5x + 2)/(3x - 4) dx` = ______
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate:
`int sin^2(x/2)dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
