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Solving integrals/ z^3

Integral of z^3 dz

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 1 + I     
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 0
∫01+iz3 dz\int\limits_{0}^{1 + i} z^{3}\, dz 
Integral(z^3, (z, 0, 1 + i))
Detail solution

  1. The integral of znz^{n} is zn+1n+1\frac{z^{n + 1}}{n + 1} when n≠−1n \neq -1:

    ∫z3 dz=z44\int z^{3}\, dz = \frac{z^{4}}{4}

  2. Add the constant of integration:

    z44+constant\frac{z^{4}}{4}+ \mathrm{constant}

The answer is:

z44+constant\frac{z^{4}}{4}+ \mathrm{constant}

The answer [src] 
       4
(1 + I) 
--------
   4
(1+i)44\frac{\left(1 + i\right)^{4}}{4} 
=
= 
       4
(1 + I) 
--------
   4
(1+i)44\frac{\left(1 + i\right)^{4}}{4} 
(1 + i)^4/4
Numerical answer [src] 
(-1.0 + 0.0j)
(-1.0 + 0.0j)

    Use the examples entering the upper and lower limits of integration.

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