Advertisements
Advertisements
Question
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Advertisements
Solution
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
RELATED QUESTIONS
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).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)/(cosx - sinx).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
`int logx/(log ex)^2*dx` = ______.
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int 1/(xsin^2(logx)) "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
Evaluate `int(3x^2 - 5)^2 "d"x`
`int x^3"e"^(x^2) "d"x`
`int sin^-1 x`dx = ?
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate `int(1 + x + x^2/(2!) )dx`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
