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: `int(x+3)sqrt(3-4x-x^2dx)`
Integrate the functions:
`1/(1 + cot x)`
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
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
The value of `intsinx/(sinx - cosx)dx` equals ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
`int "cosec"^4x dx` = ______.
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
