Advertisements
Advertisements
प्रश्न
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Advertisements
उत्तर
`int (1)/sqrt(2x^2 - 5).dx`
= `(1)/sqrt(2) int (1)/sqrt(x^2 - 5/2).dx`
= `(1)/sqrt(2) int (1)/sqrt(x^2 - (sqrt(5/2))^2).dx`
= `(1)/sqrt(2) log|x + sqrt(x^2 - 5/2)| + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`sin x/(1+ cos x)`
Integrate the functions:
`(1+ log x)^2/x`
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Integrate the following w.r.t. x : x3 + x2 – x + 1
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : tan5x
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int 1/(cos x - sin x)` dx = _______________
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int(1 - x)^(-2) dx` = ______.
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
Write `int cotx dx`.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
Evaluate `int1/(x(x - 1))dx`
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
