Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
atan(sqrt(2)*pi^4*K^4*(6*sqrt(2)/(pi*K)+18*sqrt(2)/(pi^3*K^3))/36)
¿Cómo vas a descomponer esta atan(sqrt(2)*pi^4*K^4*(6*sqrt(2)/(pi*K)+18*sqrt(2)/(pi^3*K^3))/36) expresión en fracciones?
Solución
Ha introducido
[src]
/ / ___ ___\\
| ___ 4 4 |6*\/ 2 18*\/ 2 ||
|\/ 2 *pi *k *|------- + --------||
| | pi*k 3 3 ||
| \ pi *k /|
atan|---------------------------------|
\ 36 /
$$\operatorname{atan}{\left(\frac{k^{4} \sqrt{2} \pi^{4} \left(\frac{18 \sqrt{2}}{\pi^{3} k^{3}} + \frac{6 \sqrt{2}}{\pi k}\right)}{36} \right)}$$
atan((((sqrt(2)*pi^4)*k^4)*((6*sqrt(2))/((pi*k)) + (18*sqrt(2))/((pi^3*k^3))))/36)
Simplificación general
[src]
/ 3 3\
| pi *k |
atan|pi*k + ------|
\ 3 /
$$\operatorname{atan}{\left(\frac{\pi^{3} k^{3}}{3} + \pi k \right)}$$
atan(pi*k + pi^3*k^3/3)
Descomposición de una fracción
[src]
atan(pi*k + pi^3*k^3/3)
$$\operatorname{atan}{\left(\frac{\pi^{3} k^{3}}{3} + \pi k \right)}$$
/ 3 3\
| pi *k |
atan|pi*k + ------|
\ 3 /
Potencias
[src]
/ / ___ ___ \\
| ___ 4 4 | \/ 2 \/ 2 ||
atan|\/ 2 *pi *k *|-------- + ------||
| | 3 3 6*pi*k||
\ \2*pi *k //
$$\operatorname{atan}{\left(\sqrt{2} \pi^{4} k^{4} \left(\frac{\sqrt{2}}{6 \pi k} + \frac{\sqrt{2}}{2 \pi^{3} k^{3}}\right) \right)}$$
/ / ___ ___\\
| ___ 4 4 |6*\/ 2 18*\/ 2 ||
|\/ 2 *pi *k *|------- + --------||
| | pi*k 3 3 ||
| \ pi *k /|
atan|---------------------------------|
\ 36 /
$$\operatorname{atan}{\left(\frac{\sqrt{2} \pi^{4} k^{4} \left(\frac{6 \sqrt{2}}{\pi k} + \frac{18 \sqrt{2}}{\pi^{3} k^{3}}\right)}{36} \right)}$$
atan(sqrt(2)*pi^4*k^4*(6*sqrt(2)/(pi*k) + 18*sqrt(2)/(pi^3*k^3))/36)
Respuesta numérica
[src]
atan((((sqrt(2)*pi^4)*k^4)*((6*sqrt(2))/((pi*k)) + (18*sqrt(2))/((pi^3*k^3))))/36)
atan((((sqrt(2)*pi^4)*k^4)*((6*sqrt(2))/((pi*k)) + (18*sqrt(2))/((pi^3*k^3))))/36)
Parte trigonométrica
[src]
/ / ___ ___\\
| ___ 4 4 |6*\/ 2 18*\/ 2 ||
|\/ 2 *pi *k *|------- + --------||
| | pi*k 3 3 ||
| \ pi *k /|
atan|---------------------------------|
\ 36 /
$$\operatorname{atan}{\left(\frac{\sqrt{2} \pi^{4} k^{4} \left(\frac{6 \sqrt{2}}{\pi k} + \frac{18 \sqrt{2}}{\pi^{3} k^{3}}\right)}{36} \right)}$$
atan(sqrt(2)*pi^4*k^4*(6*sqrt(2)/(pi*k) + 18*sqrt(2)/(pi^3*k^3))/36)
Unión de expresiones racionales
[src]
/ / 2 2\\
|pi*k*\3 + pi *k /|
atan|-----------------|
\ 3 /
$$\operatorname{atan}{\left(\frac{\pi k \left(\pi^{2} k^{2} + 3\right)}{3} \right)}$$
atan(pi*k*(3 + pi^2*k^2)/3)
Combinatoria
[src]
/ 3 3\
| pi *k |
atan|pi*k + ------|
\ 3 /
$$\operatorname{atan}{\left(\frac{\pi^{3} k^{3}}{3} + \pi k \right)}$$
atan(pi*k + pi^3*k^3/3)
Denominador común
[src]
/ 3 3\
| pi *k |
atan|pi*k + ------|
\ 3 /
$$\operatorname{atan}{\left(\frac{\pi^{3} k^{3}}{3} + \pi k \right)}$$
atan(pi*k + pi^3*k^3/3)
Denominador racional
[src]
/ / 2 2\\
|pi*k*\3 + pi *k /|
atan|-----------------|
\ 3 /
$$\operatorname{atan}{\left(\frac{\pi k \left(\pi^{2} k^{2} + 3\right)}{3} \right)}$$
atan(pi*k*(3 + pi^2*k^2)/3)