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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
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- Differential equations Step by Step
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How to use it?
- Integral of d{x}:
- Integral of x^2*ln(x)
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Integral of -4
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Integral of 1/2x^2
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Integral of 2sinxcosx
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Identical expressions
- z- one /(x*y*z^ two)
- z minus 1 divide by (x multiply by y multiply by z squared )
- z minus one divide by (x multiply by y multiply by z to the power of two)
- z-1/(x*y*z2)
- z-1/x*y*z2
- z-1/(x*y*z²)
- z-1/(x*y*z to the power of 2)
- z-1/(xyz^2)
- z-1/(xyz2)
- z-1/xyz2
- z-1/xyz^2
- z-1 divide by (x*y*z^2)
- z-1/(x*y*z^2)dx
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Similar expressions
- z+1/(x*y*z^2)
Integral of z-1/(x*y*z^2) dz
The solution
You have entered
[src]
z / | | / 1 \ | |z - ------| dz | | 2| | \ x*y*z / | / 0
$$\int\limits_{0}^{z} \left(z - \frac{1}{z^{2} x y}\right)\, dz$$
Integral(z - 1/((x*y)*z^2), (z, 0, z))
Detail solution
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Integrate term-by-term:
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The integral of is when :
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The integral of a constant times a function is the constant times the integral of the function:
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The integral of is .
So, the result is:
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The result is:
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Add the constant of integration:
The answer is:
The answer (Indefinite)
[src]
/ | 2 | / 1 \ z zoo*atan(zoo*z) | |z - ------| dz = C + -- + --------------- | | 2| 2 x*y | \ x*y*z / | /
$$\int \left(z - \frac{1}{z^{2} x y}\right)\, dz = C + \frac{z^{2}}{2} + \frac{\tilde{\infty} \operatorname{atan}{\left(\tilde{\infty} z \right)}}{x y}$$
The answer
[src]
2
1 x*y*z
- + ------
/ 1 \ z 2
- oo*sign|---| + ----------
\x*y/ x*y
$$- \infty \operatorname{sign}{\left(\frac{1}{x y} \right)} + \frac{\frac{x y z^{2}}{2} + \frac{1}{z}}{x y}$$
=
=
2
1 x*y*z
- + ------
/ 1 \ z 2
- oo*sign|---| + ----------
\x*y/ x*y
$$- \infty \operatorname{sign}{\left(\frac{1}{x y} \right)} + \frac{\frac{x y z^{2}}{2} + \frac{1}{z}}{x y}$$
-oo*sign(1/(x*y)) + (1/z + x*y*z^2/2)/(x*y)
Use the examples entering the upper and lower limits of integration.