Sr Examen
Integral de 9/((x-5)(x^2+2+10)) dx
Solución
Ha introducido
[src]
1 / | | 9 | --------------------- dx | / 2 \ | (x - 5)*\x + 2 + 10/ | / 0
$$\int\limits_{0}^{1} \frac{9}{\left(x - 5\right) \left(\left(x^{2} + 2\right) + 10\right)}\, dx$$
Integral(9/(((x - 5)*(x^2 + 2 + 10))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___\ / ___ |x*\/ 3 | | / 2\ 15*\/ 3 *atan|-------| | 9 9*log\12 + x / 9*log(-5 + x) \ 6 / | --------------------- dx = C - -------------- + ------------- - ---------------------- | / 2 \ 74 37 74 | (x - 5)*\x + 2 + 10/ | /
$$\int \frac{9}{\left(x - 5\right) \left(\left(x^{2} + 2\right) + 10\right)}\, dx = C + \frac{9 \log{\left(x - 5 \right)}}{37} - \frac{9 \log{\left(x^{2} + 12 \right)}}{74} - \frac{15 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{6} \right)}}{74}$$
Gráfica
Respuesta
[src]
/ ___\
___ |\/ 3 |
15*\/ 3 *atan|-----|
9*log(5) 9*log(13) 9*log(4) 9*log(12) \ 6 /
- -------- - --------- + -------- + --------- - --------------------
37 74 37 74 74
$$- \frac{9 \log{\left(5 \right)}}{37} - \frac{9 \log{\left(13 \right)}}{74} - \frac{15 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{6} \right)}}{74} + \frac{9 \log{\left(12 \right)}}{74} + \frac{9 \log{\left(4 \right)}}{37}$$
=
=
/ ___\
___ |\/ 3 |
15*\/ 3 *atan|-----|
9*log(5) 9*log(13) 9*log(4) 9*log(12) \ 6 /
- -------- - --------- + -------- + --------- - --------------------
37 74 37 74 74
$$- \frac{9 \log{\left(5 \right)}}{37} - \frac{9 \log{\left(13 \right)}}{74} - \frac{15 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{6} \right)}}{74} + \frac{9 \log{\left(12 \right)}}{74} + \frac{9 \log{\left(4 \right)}}{37}$$
-9*log(5)/37 - 9*log(13)/74 + 9*log(4)/37 + 9*log(12)/74 - 15*sqrt(3)*atan(sqrt(3)/6)/74
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.