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