Sr Examen
Integral de sh(x)^4 dx
Solución
Ha introducido
[src]
log(2)
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0
$$\int\limits_{0}^{\log{\left(2 \right)}} \sinh^{4}{\left(x \right)}\, dx$$
Integral(sinh(x)^4, (x, 0, log(2)))
Respuesta (Indefinida)
[src]
/ | 3 4 4 3 2 2 | 4 3*cosh (x)*sinh(x) 3*x*cosh (x) 3*x*sinh (x) 5*sinh (x)*cosh(x) 3*x*cosh (x)*sinh (x) | sinh (x) dx = C - ------------------ + ------------ + ------------ + ------------------ - --------------------- | 8 8 8 8 4 /
$$\int \sinh^{4}{\left(x \right)}\, dx = C + \frac{3 x \sinh^{4}{\left(x \right)}}{8} - \frac{3 x \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}}{4} + \frac{3 x \cosh^{4}{\left(x \right)}}{8} + \frac{5 \sinh^{3}{\left(x \right)} \cosh{\left(x \right)}}{8} - \frac{3 \sinh{\left(x \right)} \cosh^{3}{\left(x \right)}}{8}$$
Gráfica
Respuesta
[src]
3 4 4 3 2 2
3*cosh (log(2))*sinh(log(2)) 3*cosh (log(2))*log(2) 3*sinh (log(2))*log(2) 5*sinh (log(2))*cosh(log(2)) 3*cosh (log(2))*sinh (log(2))*log(2)
- ---------------------------- + ---------------------- + ---------------------- + ---------------------------- - ------------------------------------
8 8 8 8 4
$$- \frac{3 \sinh{\left(\log{\left(2 \right)} \right)} \cosh^{3}{\left(\log{\left(2 \right)} \right)}}{8} - \frac{3 \log{\left(2 \right)} \sinh^{2}{\left(\log{\left(2 \right)} \right)} \cosh^{2}{\left(\log{\left(2 \right)} \right)}}{4} + \frac{3 \log{\left(2 \right)} \sinh^{4}{\left(\log{\left(2 \right)} \right)}}{8} + \frac{5 \sinh^{3}{\left(\log{\left(2 \right)} \right)} \cosh{\left(\log{\left(2 \right)} \right)}}{8} + \frac{3 \log{\left(2 \right)} \cosh^{4}{\left(\log{\left(2 \right)} \right)}}{8}$$
=
=
3 4 4 3 2 2
3*cosh (log(2))*sinh(log(2)) 3*cosh (log(2))*log(2) 3*sinh (log(2))*log(2) 5*sinh (log(2))*cosh(log(2)) 3*cosh (log(2))*sinh (log(2))*log(2)
- ---------------------------- + ---------------------- + ---------------------- + ---------------------------- - ------------------------------------
8 8 8 8 4
$$- \frac{3 \sinh{\left(\log{\left(2 \right)} \right)} \cosh^{3}{\left(\log{\left(2 \right)} \right)}}{8} - \frac{3 \log{\left(2 \right)} \sinh^{2}{\left(\log{\left(2 \right)} \right)} \cosh^{2}{\left(\log{\left(2 \right)} \right)}}{4} + \frac{3 \log{\left(2 \right)} \sinh^{4}{\left(\log{\left(2 \right)} \right)}}{8} + \frac{5 \sinh^{3}{\left(\log{\left(2 \right)} \right)} \cosh{\left(\log{\left(2 \right)} \right)}}{8} + \frac{3 \log{\left(2 \right)} \cosh^{4}{\left(\log{\left(2 \right)} \right)}}{8}$$
-3*cosh(log(2))^3*sinh(log(2))/8 + 3*cosh(log(2))^4*log(2)/8 + 3*sinh(log(2))^4*log(2)/8 + 5*sinh(log(2))^3*cosh(log(2))/8 - 3*cosh(log(2))^2*sinh(log(2))^2*log(2)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.