Sr Examen
Integral de (sin(3x^2)-3x^2)/(7x^6) dx
Solución
Ha introducido
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1/3 / | | / 2\ 2 | sin\3*x / - 3*x | ---------------- dx | 6 | 7*x | / 0
$$\int\limits_{0}^{\frac{1}{3}} \frac{- 3 x^{2} + \sin{\left(3 x^{2} \right)}}{7 x^{6}}\, dx$$
Integral((sin(3*x^2) - 3*x^2)/((7*x^6)), (x, 0, 1/3))
Respuesta (Indefinida)
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/ ___\ / ___ ____ |x*\/ 6 | | 9*\/ 6 *\/ pi *C|-------|*Gamma(-3/4) | / 2\ 2 / 2\ / 2\ / 2\ | ____| | sin\3*x / - 3*x 1 9*Gamma(-3/4)*sin\3*x / 3*cos\3*x /*Gamma(-3/4) 3*Gamma(-3/4)*sin\3*x / \ \/ pi / | ---------------- dx = C + ---- - ----------------------- + ----------------------- + ----------------------- + ------------------------------------- | 6 3 35*x*Gamma(1/4) 3 5 35*Gamma(1/4) | 7*x 7*x 70*x *Gamma(1/4) 140*x *Gamma(1/4) | /
$$\int \frac{- 3 x^{2} + \sin{\left(3 x^{2} \right)}}{7 x^{6}}\, dx = C + \frac{9 \sqrt{6} \sqrt{\pi} C\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right) \Gamma\left(- \frac{3}{4}\right)}{35 \Gamma\left(\frac{1}{4}\right)} - \frac{9 \sin{\left(3 x^{2} \right)} \Gamma\left(- \frac{3}{4}\right)}{35 x \Gamma\left(\frac{1}{4}\right)} + \frac{3 \cos{\left(3 x^{2} \right)} \Gamma\left(- \frac{3}{4}\right)}{70 x^{3} \Gamma\left(\frac{1}{4}\right)} + \frac{1}{7 x^{3}} + \frac{3 \sin{\left(3 x^{2} \right)} \Gamma\left(- \frac{3}{4}\right)}{140 x^{5} \Gamma\left(\frac{1}{4}\right)}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.