Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of √xdx
-
Integral of √(1-x^2)
-
Integral of 1/(2x)
-
Integral of (e^x)/x
-
Identical expressions
- one /(z^ four + one)
- 1 divide by (z to the power of 4 plus 1)
- one divide by (z to the power of four plus one)
- 1/(z4+1)
- 1/z4+1
- 1/(z⁴+1)
- 1/z^4+1
- 1 divide by (z^4+1)
-
Similar expressions
- 1/(z^4-1)
Integral of 1/(z^4+1) dx
The solution
You have entered
[src]
1 / | | 1 | ------ dz | 4 | z + 1 | / 0
$$\int\limits_{0}^{1} \frac{1}{z^{4} + 1}\, dz$$
Integral(1/(z^4 + 1), (z, 0, 1))
The answer (Indefinite)
[src]
/ | ___ / 2 ___\ ___ / ___\ ___ / ___\ ___ / 2 ___\ | 1 \/ 2 *log\1 + z - z*\/ 2 / \/ 2 *atan\1 + z*\/ 2 / \/ 2 *atan\-1 + z*\/ 2 / \/ 2 *log\1 + z + z*\/ 2 / | ------ dz = C - --------------------------- + ----------------------- + ------------------------ + --------------------------- | 4 8 4 4 8 | z + 1 | /
$$\int \frac{1}{z^{4} + 1}\, dz = C - \frac{\sqrt{2} \log{\left(z^{2} - \sqrt{2} z + 1 \right)}}{8} + \frac{\sqrt{2} \log{\left(z^{2} + \sqrt{2} z + 1 \right)}}{8} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} z - 1 \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} z + 1 \right)}}{4}$$
The graph
The answer
[src]
___ / ___\ ___ ___ / ___\
\/ 2 *log\2 - \/ 2 / pi*\/ 2 \/ 2 *log\2 + \/ 2 /
- -------------------- + -------- + --------------------
8 8 8
$$- \frac{\sqrt{2} \log{\left(2 - \sqrt{2} \right)}}{8} + \frac{\sqrt{2} \log{\left(\sqrt{2} + 2 \right)}}{8} + \frac{\sqrt{2} \pi}{8}$$
=
=
___ / ___\ ___ ___ / ___\
\/ 2 *log\2 - \/ 2 / pi*\/ 2 \/ 2 *log\2 + \/ 2 /
- -------------------- + -------- + --------------------
8 8 8
$$- \frac{\sqrt{2} \log{\left(2 - \sqrt{2} \right)}}{8} + \frac{\sqrt{2} \log{\left(\sqrt{2} + 2 \right)}}{8} + \frac{\sqrt{2} \pi}{8}$$
-sqrt(2)*log(2 - sqrt(2))/8 + pi*sqrt(2)/8 + sqrt(2)*log(2 + sqrt(2))/8
Use the examples entering the upper and lower limits of integration.