Sr Examen
Integral de sin(2x)/(sqrt((sinx)^4-9)) dx
Solución
Ha introducido
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1 / | | sin(2*x) | ---------------- dx | _____________ | / 4 | \/ sin (x) - 9 | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(2 x \right)}}{\sqrt{\sin^{4}{\left(x \right)} - 9}}\, dx$$
Integral(sin(2*x)/sqrt(sin(x)^4 - 9), (x, 0, 1))
Respuesta (Indefinida)
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/ / | | | sin(2*x) | cos(x)*sin(x) | ---------------- dx = C + 2* | --------------------------------- dx | _____________ | ______________________________ | / 4 | / / 2 \ / 2 \ | \/ sin (x) - 9 | \/ \-3 + sin (x)/*\3 + sin (x)/ | | / /
$$\int \frac{\sin{\left(2 x \right)}}{\sqrt{\sin^{4}{\left(x \right)} - 9}}\, dx = C + 2 \int \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{\left(\sin^{2}{\left(x \right)} - 3\right) \left(\sin^{2}{\left(x \right)} + 3\right)}}\, dx$$
Respuesta
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1 / | | sin(2*x) | ---------------------------------- dx | ______________ _____________ | / 2 / 2 | \/ -3 + sin (x) *\/ 3 + sin (x) | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(2 x \right)}}{\sqrt{\sin^{2}{\left(x \right)} - 3} \sqrt{\sin^{2}{\left(x \right)} + 3}}\, dx$$
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1 / | | sin(2*x) | ---------------------------------- dx | ______________ _____________ | / 2 / 2 | \/ -3 + sin (x) *\/ 3 + sin (x) | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(2 x \right)}}{\sqrt{\sin^{2}{\left(x \right)} - 3} \sqrt{\sin^{2}{\left(x \right)} + 3}}\, dx$$
Integral(sin(2*x)/(sqrt(-3 + sin(x)^2)*sqrt(3 + sin(x)^2)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.