Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Advertisements
उत्तर
Let I = `int ((sin^-1 x)^(3/2))/sqrt(1 - x^2).dx`
Put sin–1x = t.
∴ `(1)/sqrt(1 - x^2).dx` = dt
∴ I = `int t^(3/2)dt`
= `t^(5/2)/(5/2) + c`
= `(2)/(5)(sin^-1x)^(5/2) + c`.
APPEARS IN
संबंधित प्रश्न
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`x/(9 - 4x^2)`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
`int "dx"/(9"x"^2 + 1)= ______. `
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
`int logx/(log ex)^2*dx` = ______.
Evaluate `int (3"x"^2 - 5)^2` dx
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Evaluate `int (5"x" + 1)^(4/9)` dx
`int 1/(cos x - sin x)` dx = _______________
`int (log x)/(log ex)^2` dx = _________
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int (cos x)/(1 - sin x) "dx" =` ______.
`int sec^6 x tan x "d"x` = ______.
`int cos^3x dx` = ______.
Write `int cotx dx`.
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int1/(x(x - 1))dx`
