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