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 1/(x(1-x))
-
Integral of x*ln(x^2+1)
- Integral of ln(x+(1+x^2)^(1/2))
-
Integral of e^(-x)*cos(3*x)
-
Identical expressions
- dx/(x^ four + one)
- dx divide by (x to the power of 4 plus 1)
- dx divide by (x to the power of four plus one)
- dx/(x4+1)
- dx/x4+1
- dx/(x⁴+1)
- dx/x^4+1
- dx divide by (x^4+1)
-
Similar expressions
- dx/(x^4-1)
Integral of dx/(x^4+1) dx
The solution
You have entered
[src]
___ \/ 3 / | | 1 | ------ dx | 4 | x + 1 | / ___ \/ 3 ----- 3
$$\int\limits_{\frac{\sqrt{3}}{3}}^{\sqrt{3}} \frac{1}{x^{4} + 1}\, dx$$
Integral(1/(x^4 + 1), (x, sqrt(3)/3, sqrt(3)))
The answer (Indefinite)
[src]
/ | ___ / 2 ___\ ___ / ___\ ___ / ___\ ___ / 2 ___\ | 1 \/ 2 *log\1 + x - x*\/ 2 / \/ 2 *atan\1 + x*\/ 2 / \/ 2 *atan\-1 + x*\/ 2 / \/ 2 *log\1 + x + x*\/ 2 / | ------ dx = C - --------------------------- + ----------------------- + ------------------------ + --------------------------- | 4 8 4 4 8 | x + 1 | /
$$\int \frac{1}{x^{4} + 1}\, dx = C - \frac{\sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{8} + \frac{\sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{8} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{4}$$
The graph
The answer
[src]
/ ___\ / ___\ / ___\ / ___\
___ | \/ 6 | ___ |4 \/ 6 | ___ | \/ 6 | ___ |4 \/ 6 |
___ / ___\ \/ 2 *atan|1 + -----| ___ / ___\ \/ 2 *log|- + -----| ___ / ___\ \/ 2 *atan|1 - -----| ___ / ___\ \/ 2 *log|- - -----|
\/ 2 *atan\1 - \/ 6 / \ 3 / \/ 2 *log\4 - \/ 6 / \3 3 / \/ 2 *atan\1 + \/ 6 / \ 3 / \/ 2 *log\4 + \/ 6 / \3 3 /
- --------------------- - --------------------- - -------------------- - -------------------- + --------------------- + --------------------- + -------------------- + --------------------
4 4 8 8 4 4 8 8
$$- \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{6}}{3} + 1 \right)}}{4} - \frac{\sqrt{2} \log{\left(\frac{\sqrt{6}}{3} + \frac{4}{3} \right)}}{8} + \frac{\sqrt{2} \log{\left(\frac{4}{3} - \frac{\sqrt{6}}{3} \right)}}{8} - \frac{\sqrt{2} \log{\left(4 - \sqrt{6} \right)}}{8} + \frac{\sqrt{2} \operatorname{atan}{\left(1 - \frac{\sqrt{6}}{3} \right)}}{4} + \frac{\sqrt{2} \log{\left(\sqrt{6} + 4 \right)}}{8} - \frac{\sqrt{2} \operatorname{atan}{\left(1 - \sqrt{6} \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(1 + \sqrt{6} \right)}}{4}$$
=
=
/ ___\ / ___\ / ___\ / ___\
___ | \/ 6 | ___ |4 \/ 6 | ___ | \/ 6 | ___ |4 \/ 6 |
___ / ___\ \/ 2 *atan|1 + -----| ___ / ___\ \/ 2 *log|- + -----| ___ / ___\ \/ 2 *atan|1 - -----| ___ / ___\ \/ 2 *log|- - -----|
\/ 2 *atan\1 - \/ 6 / \ 3 / \/ 2 *log\4 - \/ 6 / \3 3 / \/ 2 *atan\1 + \/ 6 / \ 3 / \/ 2 *log\4 + \/ 6 / \3 3 /
- --------------------- - --------------------- - -------------------- - -------------------- + --------------------- + --------------------- + -------------------- + --------------------
4 4 8 8 4 4 8 8
$$- \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{6}}{3} + 1 \right)}}{4} - \frac{\sqrt{2} \log{\left(\frac{\sqrt{6}}{3} + \frac{4}{3} \right)}}{8} + \frac{\sqrt{2} \log{\left(\frac{4}{3} - \frac{\sqrt{6}}{3} \right)}}{8} - \frac{\sqrt{2} \log{\left(4 - \sqrt{6} \right)}}{8} + \frac{\sqrt{2} \operatorname{atan}{\left(1 - \frac{\sqrt{6}}{3} \right)}}{4} + \frac{\sqrt{2} \log{\left(\sqrt{6} + 4 \right)}}{8} - \frac{\sqrt{2} \operatorname{atan}{\left(1 - \sqrt{6} \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(1 + \sqrt{6} \right)}}{4}$$
-sqrt(2)*atan(1 - sqrt(6))/4 - sqrt(2)*atan(1 + sqrt(6)/3)/4 - sqrt(2)*log(4 - sqrt(6))/8 - sqrt(2)*log(4/3 + sqrt(6)/3)/8 + sqrt(2)*atan(1 + sqrt(6))/4 + sqrt(2)*atan(1 - sqrt(6)/3)/4 + sqrt(2)*log(4 + sqrt(6))/8 + sqrt(2)*log(4/3 - sqrt(6)/3)/8
Use the examples entering the upper and lower limits of integration.