Advertisements
Advertisements
प्रश्न
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Advertisements
उत्तर
Let `x^(3/2)` = t
`\implies` dt = `3/2 x^(1/2) dx`
`int sqrt(x/(1 - x^3))dx = 2/3 int dt/sqrt(1 - t^2)`
= `2/3 sin^-1 (t) + c`
= `2/3 sin^-1 (x^(3/2)) + c`, where 'c' is an arbitrary constant of integration.
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int "x" * "e"^"2x"` dx
Evaluate: `int "e"^sqrt"x"` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int x/(x + 2) "d"x`
`int(log(logx))/x "d"x`
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
`int 1/(sinx.cos^2x)dx` = ______.
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
