Mister Exam
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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of x*e^(x*(-2))
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Integral of 1/(2+3x^2)
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Integral of x(x+1)^1/2
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Integral of (x^3-1)^1/2
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Identical expressions
- sqrt(y)/((y^ three)- one)
- square root of (y) divide by ((y cubed ) minus 1)
- square root of (y) divide by ((y to the power of three) minus one)
- √(y)/((y^3)-1)
- sqrt(y)/((y3)-1)
- sqrty/y3-1
- sqrt(y)/((y³)-1)
- sqrt(y)/((y to the power of 3)-1)
- sqrty/y^3-1
- sqrt(y) divide by ((y^3)-1)
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Similar expressions
- sqrt(y)/((y^3)+1)
Integral of sqrt(y)/((y^3)-1) dy
The solution
You have entered
[src]
1 / | | ___ | \/ y | ------ dy | 3 | y - 1 | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{y}}{y^{3} - 1}\, dy$$
Integral(sqrt(y)/(y^3 - 1), (y, 0, 1))
The answer (Indefinite)
[src]
/ // / 3/2\ \ | ||-acoth\y / 3 | | ___ ||------------- for y > 1| | \/ y || 3 | | ------ dy = C + 2*|< | | 3 || / 3/2\ | | y - 1 ||-atanh\y / 3 | | ||------------- for y < 1| / \\ 3 /
$$\int \frac{\sqrt{y}}{y^{3} - 1}\, dy = C + 2 \left(\begin{cases} - \frac{\operatorname{acoth}{\left(y^{\frac{3}{2}} \right)}}{3} & \text{for}\: y^{3} > 1 \\- \frac{\operatorname{atanh}{\left(y^{\frac{3}{2}} \right)}}{3} & \text{for}\: y^{3} < 1 \end{cases}\right)$$
The graph
The answer
[src]
pi*I
-oo - ----
3
$$-\infty - \frac{i \pi}{3}$$
=
=
pi*I
-oo - ----
3
$$-\infty - \frac{i \pi}{3}$$
-oo - pi*i/3
Use the examples entering the upper and lower limits of integration.