Sr Examen
Integral de (9*x^3-4)/(x^3+27) dx
Solución
Ha introducido
[src]
1 / | | 3 | 9*x - 4 | -------- dx | 3 | x + 27 | / 0
$$\int\limits_{0}^{1} \frac{9 x^{3} - 4}{x^{3} + 27}\, dx$$
Integral((9*x^3 - 4)/(x^3 + 27), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ___ \ | ___ |2*\/ 3 *(-3/2 + x)| | 3 / 2 \ 247*\/ 3 *atan|------------------| | 9*x - 4 247*log(3 + x) 247*log\9 + x - 3*x/ \ 9 / | -------- dx = C + 9*x - -------------- + --------------------- - ---------------------------------- | 3 27 54 27 | x + 27 | /
$$\int \frac{9 x^{3} - 4}{x^{3} + 27}\, dx = C + 9 x - \frac{247 \log{\left(x + 3 \right)}}{27} + \frac{247 \log{\left(x^{2} - 3 x + 9 \right)}}{54} - \frac{247 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x - \frac{3}{2}\right)}{9} \right)}}{27}$$
Gráfica
Respuesta
[src]
/ ___\
___ |\/ 3 |
___ 247*\/ 3 *atan|-----|
247*log(4) 247*log(9) 247*log(3) 247*log(7) 247*pi*\/ 3 \ 9 /
9 - ---------- - ---------- + ---------- + ---------- - ------------ + ---------------------
27 54 27 54 162 27
$$- \frac{247 \log{\left(4 \right)}}{27} - \frac{247 \log{\left(9 \right)}}{54} - \frac{247 \sqrt{3} \pi}{162} + \frac{247 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{9} \right)}}{27} + \frac{247 \log{\left(7 \right)}}{54} + 9 + \frac{247 \log{\left(3 \right)}}{27}$$
=
=
/ ___\
___ |\/ 3 |
___ 247*\/ 3 *atan|-----|
247*log(4) 247*log(9) 247*log(3) 247*log(7) 247*pi*\/ 3 \ 9 /
9 - ---------- - ---------- + ---------- + ---------- - ------------ + ---------------------
27 54 27 54 162 27
$$- \frac{247 \log{\left(4 \right)}}{27} - \frac{247 \log{\left(9 \right)}}{54} - \frac{247 \sqrt{3} \pi}{162} + \frac{247 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{9} \right)}}{27} + \frac{247 \log{\left(7 \right)}}{54} + 9 + \frac{247 \log{\left(3 \right)}}{27}$$
9 - 247*log(4)/27 - 247*log(9)/54 + 247*log(3)/27 + 247*log(7)/54 - 247*pi*sqrt(3)/162 + 247*sqrt(3)*atan(sqrt(3)/9)/27
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.