Sr Examen
Integral de cosh^3(x/5) dx
Solución
Ha introducido
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1 / | | 3/x\ | cosh |-| dx | \5/ | / 0
$$\int\limits_{0}^{1} \cosh^{3}{\left(\frac{x}{5} \right)}\, dx$$
Integral(cosh(x/5)^3, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 5/x \ /x \ 3/x \ | 30*tanh |--| 30*tanh|--| 20*tanh |--| | 3/x\ \10/ \10/ \10/ | cosh |-| dx = C - -------------------------------------------- - -------------------------------------------- + -------------------------------------------- | \5/ 4/x \ 6/x \ 2/x \ 4/x \ 6/x \ 2/x \ 4/x \ 6/x \ 2/x \ | -3 - 9*tanh |--| + 3*tanh |--| + 9*tanh |--| -3 - 9*tanh |--| + 3*tanh |--| + 9*tanh |--| -3 - 9*tanh |--| + 3*tanh |--| + 9*tanh |--| / \10/ \10/ \10/ \10/ \10/ \10/ \10/ \10/ \10/
$$\int \cosh^{3}{\left(\frac{x}{5} \right)}\, dx = C - \frac{30 \tanh^{5}{\left(\frac{x}{10} \right)}}{3 \tanh^{6}{\left(\frac{x}{10} \right)} - 9 \tanh^{4}{\left(\frac{x}{10} \right)} + 9 \tanh^{2}{\left(\frac{x}{10} \right)} - 3} + \frac{20 \tanh^{3}{\left(\frac{x}{10} \right)}}{3 \tanh^{6}{\left(\frac{x}{10} \right)} - 9 \tanh^{4}{\left(\frac{x}{10} \right)} + 9 \tanh^{2}{\left(\frac{x}{10} \right)} - 3} - \frac{30 \tanh{\left(\frac{x}{10} \right)}}{3 \tanh^{6}{\left(\frac{x}{10} \right)} - 9 \tanh^{4}{\left(\frac{x}{10} \right)} + 9 \tanh^{2}{\left(\frac{x}{10} \right)} - 3}$$
Gráfica
Respuesta
[src]
3
10*sinh (1/5) 2
- ------------- + 5*cosh (1/5)*sinh(1/5)
3
$$- \frac{10 \sinh^{3}{\left(\frac{1}{5} \right)}}{3} + 5 \sinh{\left(\frac{1}{5} \right)} \cosh^{2}{\left(\frac{1}{5} \right)}$$
=
=
3
10*sinh (1/5) 2
- ------------- + 5*cosh (1/5)*sinh(1/5)
3
$$- \frac{10 \sinh^{3}{\left(\frac{1}{5} \right)}}{3} + 5 \sinh{\left(\frac{1}{5} \right)} \cosh^{2}{\left(\frac{1}{5} \right)}$$
-10*sinh(1/5)^3/3 + 5*cosh(1/5)^2*sinh(1/5)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.