Advertisements
Advertisements
प्रश्न
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
पर्याय
`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
उत्तर
`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
संबंधित प्रश्न
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`1/(1 + cot x)`
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\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `intsqrt(1 - cos 2x)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 : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate: `int log ("x"^2 + "x")` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int cot^2x "d"x`
`int(log(logx))/x "d"x`
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
`int(log(logx) + 1/(logx)^2)dx` = ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
`int (logx)^2/x dx` = ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate the following.
`int1/(x^2+4x-5) dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
