Advertisements
Advertisements
प्रश्न
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Advertisements
उत्तर
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
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Write a value of\[\int \log_e x\ dx\].
Write a value of
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Evaluate the following integrals : `intsqrt(1 + sin 5x).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 : `(1)/(x.logx.log(logx)`.
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
Evaluate `int1/(x(x - 1))dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
