Sr Examen
Integral de x/(3+Sqr(3x+4)) dx
Solución
Ha introducido
[src]
4 / | | x | -------------- dx | 2 | 3 + (3*x + 4) | / 0
$$\int\limits_{0}^{4} \frac{x}{\left(3 x + 4\right)^{2} + 3}\, dx$$
Integral(x/(3 + (3*x + 4)^2), (x, 0, 4))
Respuesta (Indefinida)
[src]
/ | / 2 \ ___ / ___ \ | x log\19 + 9*x + 24*x/ 4*\/ 3 *atan\\/ 3 *(4/3 + x)/ | -------------- dx = C + --------------------- - ----------------------------- | 2 18 27 | 3 + (3*x + 4) | /
$$\int \frac{x}{\left(3 x + 4\right)^{2} + 3}\, dx = C + \frac{\log{\left(9 x^{2} + 24 x + 19 \right)}}{18} - \frac{4 \sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(x + \frac{4}{3}\right) \right)}}{27}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\
___ |16*\/ 3 | ___ |4*\/ 3 |
4*\/ 3 *atan|--------| 4*\/ 3 *atan|-------|
log(19/9) log(259/9) \ 3 / \ 3 /
- --------- + ---------- - ---------------------- + ---------------------
18 18 27 27
$$- \frac{4 \sqrt{3} \operatorname{atan}{\left(\frac{16 \sqrt{3}}{3} \right)}}{27} - \frac{\log{\left(\frac{19}{9} \right)}}{18} + \frac{\log{\left(\frac{259}{9} \right)}}{18} + \frac{4 \sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3}}{3} \right)}}{27}$$
=
=
/ ___\ / ___\
___ |16*\/ 3 | ___ |4*\/ 3 |
4*\/ 3 *atan|--------| 4*\/ 3 *atan|-------|
log(19/9) log(259/9) \ 3 / \ 3 /
- --------- + ---------- - ---------------------- + ---------------------
18 18 27 27
$$- \frac{4 \sqrt{3} \operatorname{atan}{\left(\frac{16 \sqrt{3}}{3} \right)}}{27} - \frac{\log{\left(\frac{19}{9} \right)}}{18} + \frac{\log{\left(\frac{259}{9} \right)}}{18} + \frac{4 \sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3}}{3} \right)}}{27}$$
-log(19/9)/18 + log(259/9)/18 - 4*sqrt(3)*atan(16*sqrt(3)/3)/27 + 4*sqrt(3)*atan(4*sqrt(3)/3)/27
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.