Sr Examen
Integral de (sin2x+3)/((x^3+1)^(1/2)) dx
Solución
Ha introducido
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oo / | | sin(2*x) + 3 | ------------ dx | ________ | / 3 | \/ x + 1 | / 1
$$\int\limits_{1}^{\infty} \frac{\sin{\left(2 x \right)} + 3}{\sqrt{x^{3} + 1}}\, dx$$
Integral((sin(2*x) + 3)/sqrt(x^3 + 1), (x, 1, oo))
Respuesta (Indefinida)
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_ / / |_ /1/3, 1/2 | 3 pi*I\ | | x*Gamma(1/3)* | | | x *e | | sin(2*x) + 3 | cos(x)*sin(x) 2 1 \ 4/3 | / | ------------ dx = C + 2* | ------------------------- dx + --------------------------------------- | ________ | ______________________ Gamma(4/3) | / 3 | / / 2 \ | \/ x + 1 | \/ (1 + x)*\1 + x - x/ | | / /
$$\int \frac{\sin{\left(2 x \right)} + 3}{\sqrt{x^{3} + 1}}\, dx = C + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{\Gamma\left(\frac{4}{3}\right)} + 2 \int \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{\left(x + 1\right) \left(x^{2} - x + 1\right)}}\, dx$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.