Sr Examen
Integral de 1/(x^4+5) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------ dx | 4 | x + 5 | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{4} + 5}\, dx$$
Integral(1/(x^4 + 5), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ 3/4\ / ___ 3/4\ / ___ 4 ___ | x*\/ 2 *5 | ___ 4 ___ | x*\/ 2 *5 | | ___ 4 ___ / ___ 2 ___ 4 ___\ \/ 2 *\/ 5 *atan|1 + ------------| \/ 2 *\/ 5 *atan|-1 + ------------| ___ 4 ___ / ___ 2 ___ 4 ___\ | 1 \/ 2 *\/ 5 *log\\/ 5 + x - x*\/ 2 *\/ 5 / \ 5 / \ 5 / \/ 2 *\/ 5 *log\\/ 5 + x + x*\/ 2 *\/ 5 / | ------ dx = C - ------------------------------------------- + ---------------------------------- + ----------------------------------- + ------------------------------------------- | 4 40 20 20 40 | x + 5 | /
$$\int \frac{1}{x^{4} + 5}\, dx = C - \frac{\sqrt{2} \sqrt[4]{5} \log{\left(x^{2} - \sqrt{2} \sqrt[4]{5} x + \sqrt{5} \right)}}{40} + \frac{\sqrt{2} \sqrt[4]{5} \log{\left(x^{2} + \sqrt{2} \sqrt[4]{5} x + \sqrt{5} \right)}}{40} + \frac{\sqrt{2} \sqrt[4]{5} \operatorname{atan}{\left(\frac{\sqrt{2} \cdot 5^{\frac{3}{4}} x}{5} - 1 \right)}}{20} + \frac{\sqrt{2} \sqrt[4]{5} \operatorname{atan}{\left(\frac{\sqrt{2} \cdot 5^{\frac{3}{4}} x}{5} + 1 \right)}}{20}$$
Gráfica
Respuesta
[src]
/ ___ 3/4\ / ___ 3/4\
___ 4 ___ | \/ 2 *5 | ___ 4 ___ | \/ 2 *5 |
\/ 2 *\/ 5 *atan|1 - ----------| ___ 4 ___ / ___ ___ 4 ___\ \/ 2 *\/ 5 *atan|1 + ----------| ___ 4 ___ / ___ ___ 4 ___\
\ 5 / \/ 2 *\/ 5 *log\1 + \/ 5 - \/ 2 *\/ 5 / \ 5 / \/ 2 *\/ 5 *log\1 + \/ 5 + \/ 2 *\/ 5 /
- -------------------------------- - ---------------------------------------- + -------------------------------- + ----------------------------------------
20 40 20 40
$$- \frac{\sqrt{2} \sqrt[4]{5} \log{\left(- \sqrt{2} \sqrt[4]{5} + 1 + \sqrt{5} \right)}}{40} - \frac{\sqrt{2} \sqrt[4]{5} \operatorname{atan}{\left(- \frac{\sqrt{2} \cdot 5^{\frac{3}{4}}}{5} + 1 \right)}}{20} + \frac{\sqrt{2} \sqrt[4]{5} \log{\left(1 + \sqrt{2} \sqrt[4]{5} + \sqrt{5} \right)}}{40} + \frac{\sqrt{2} \sqrt[4]{5} \operatorname{atan}{\left(\frac{\sqrt{2} \cdot 5^{\frac{3}{4}}}{5} + 1 \right)}}{20}$$
=
=
/ ___ 3/4\ / ___ 3/4\
___ 4 ___ | \/ 2 *5 | ___ 4 ___ | \/ 2 *5 |
\/ 2 *\/ 5 *atan|1 - ----------| ___ 4 ___ / ___ ___ 4 ___\ \/ 2 *\/ 5 *atan|1 + ----------| ___ 4 ___ / ___ ___ 4 ___\
\ 5 / \/ 2 *\/ 5 *log\1 + \/ 5 - \/ 2 *\/ 5 / \ 5 / \/ 2 *\/ 5 *log\1 + \/ 5 + \/ 2 *\/ 5 /
- -------------------------------- - ---------------------------------------- + -------------------------------- + ----------------------------------------
20 40 20 40
$$- \frac{\sqrt{2} \sqrt[4]{5} \log{\left(- \sqrt{2} \sqrt[4]{5} + 1 + \sqrt{5} \right)}}{40} - \frac{\sqrt{2} \sqrt[4]{5} \operatorname{atan}{\left(- \frac{\sqrt{2} \cdot 5^{\frac{3}{4}}}{5} + 1 \right)}}{20} + \frac{\sqrt{2} \sqrt[4]{5} \log{\left(1 + \sqrt{2} \sqrt[4]{5} + \sqrt{5} \right)}}{40} + \frac{\sqrt{2} \sqrt[4]{5} \operatorname{atan}{\left(\frac{\sqrt{2} \cdot 5^{\frac{3}{4}}}{5} + 1 \right)}}{20}$$
-sqrt(2)*5^(1/4)*atan(1 - sqrt(2)*5^(3/4)/5)/20 - sqrt(2)*5^(1/4)*log(1 + sqrt(5) - sqrt(2)*5^(1/4))/40 + sqrt(2)*5^(1/4)*atan(1 + sqrt(2)*5^(3/4)/5)/20 + sqrt(2)*5^(1/4)*log(1 + sqrt(5) + sqrt(2)*5^(1/4))/40
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.