Advertisements
Advertisements
प्रश्न
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Advertisements
उत्तर
Let `I = int (sin^-1 x)/sqrt(1 - x^2)` dx
Put sin-1 x = t
`1/sqrt(1 - x^2)` dx = dt
Hence, `I = int t dt`
`=1/2t^2 + C`
`=1/2 (sin^-1 x)^2 + C`
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`sin x/(1+ cos x)`
Write a value of
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int cos sqrtx` dx = _____________
`int(1 - x)^(-2) dx` = ______.
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
