Sr Examen
Integral de sin(x)/sin4x dx
Solución
Ha introducido
[src]
1 / | | sin(x) | -------- dx | sin(4*x) | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\sin{\left(4 x \right)}}\, dx$$
Integral(sin(x)/sin(4*x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / /x\\ / ___ /x\\ / ___ /x\\ / ___ /x\\ / ___ /x\\ / /x\\ ___ / /x\\ ___ / ___ /x\\ ___ / ___ /x\\ ___ / ___ /x\\ ___ / ___ /x\\ ___ / /x\\ | 7761798*log|1 + tan|-|| 5488420*log|1 - \/ 2 + tan|-|| 5488420*log|-1 - \/ 2 + tan|-|| 5488420*log|1 + \/ 2 + tan|-|| 5488420*log|-1 + \/ 2 + tan|-|| 7761798*log|-1 + tan|-|| 5488420*\/ 2 *log|1 + tan|-|| 3880899*\/ 2 *log|1 - \/ 2 + tan|-|| 3880899*\/ 2 *log|-1 - \/ 2 + tan|-|| 3880899*\/ 2 *log|1 + \/ 2 + tan|-|| 3880899*\/ 2 *log|-1 + \/ 2 + tan|-|| 5488420*\/ 2 *log|-1 + tan|-|| | sin(x) \ \2// \ \2// \ \2// \ \2// \ \2// \ \2// \ \2// \ \2// \ \2// \ \2// \ \2// \ \2// | -------- dx = C - ------------------------- - ------------------------------- - -------------------------------- + ------------------------------- + -------------------------------- + ------------------------- - ----------------------------- - ------------------------------------- - -------------------------------------- + ------------------------------------- + -------------------------------------- + ------------------------------ | sin(4*x) ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ | 31047192 + 21953680*\/ 2 31047192 + 21953680*\/ 2 31047192 + 21953680*\/ 2 31047192 + 21953680*\/ 2 31047192 + 21953680*\/ 2 31047192 + 21953680*\/ 2 31047192 + 21953680*\/ 2 31047192 + 21953680*\/ 2 31047192 + 21953680*\/ 2 31047192 + 21953680*\/ 2 31047192 + 21953680*\/ 2 31047192 + 21953680*\/ 2 /
$$\int \frac{\sin{\left(x \right)}}{\sin{\left(4 x \right)}}\, dx = C + \frac{5488420 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{21953680 \sqrt{2} + 31047192} + \frac{7761798 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{21953680 \sqrt{2} + 31047192} - \frac{7761798 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{21953680 \sqrt{2} + 31047192} - \frac{5488420 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{21953680 \sqrt{2} + 31047192} + \frac{5488420 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{21953680 \sqrt{2} + 31047192} + \frac{3880899 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{21953680 \sqrt{2} + 31047192} + \frac{5488420 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{21953680 \sqrt{2} + 31047192} + \frac{3880899 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{21953680 \sqrt{2} + 31047192} - \frac{3880899 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{21953680 \sqrt{2} + 31047192} - \frac{5488420 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{21953680 \sqrt{2} + 31047192} - \frac{3880899 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{21953680 \sqrt{2} + 31047192} - \frac{5488420 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{21953680 \sqrt{2} + 31047192}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.