Sr Examen
Integral de (x-1)^2/(x^2+3x+4) dx
Solución
Ha introducido
[src]
1 / | | 2 | (x - 1) | ------------ dx | 2 | x + 3*x + 4 | / 0
$$\int\limits_{0}^{1} \frac{\left(x - 1\right)^{2}}{\left(x^{2} + 3 x\right) + 4}\, dx$$
Integral((x - 1)^2/(x^2 + 3*x + 4), (x, 0, 1))
Respuesta (Indefinida)
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/ / ___ \ | ___ |2*\/ 7 *(3/2 + x)| | 2 / 2 \ 9*\/ 7 *atan|-----------------| | (x - 1) 5*log\4 + x + 3*x/ \ 7 / | ------------ dx = C + x - ------------------- + ------------------------------- | 2 2 7 | x + 3*x + 4 | /
$$\int \frac{\left(x - 1\right)^{2}}{\left(x^{2} + 3 x\right) + 4}\, dx = C + x - \frac{5 \log{\left(x^{2} + 3 x + 4 \right)}}{2} + \frac{9 \sqrt{7} \operatorname{atan}{\left(\frac{2 \sqrt{7} \left(x + \frac{3}{2}\right)}{7} \right)}}{7}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\
___ |3*\/ 7 | ___ |5*\/ 7 |
9*\/ 7 *atan|-------| 9*\/ 7 *atan|-------|
5*log(8) 5*log(4) \ 7 / \ 7 /
1 - -------- + -------- - --------------------- + ---------------------
2 2 7 7
$$- \frac{5 \log{\left(8 \right)}}{2} - \frac{9 \sqrt{7} \operatorname{atan}{\left(\frac{3 \sqrt{7}}{7} \right)}}{7} + 1 + \frac{5 \log{\left(4 \right)}}{2} + \frac{9 \sqrt{7} \operatorname{atan}{\left(\frac{5 \sqrt{7}}{7} \right)}}{7}$$
=
=
/ ___\ / ___\
___ |3*\/ 7 | ___ |5*\/ 7 |
9*\/ 7 *atan|-------| 9*\/ 7 *atan|-------|
5*log(8) 5*log(4) \ 7 / \ 7 /
1 - -------- + -------- - --------------------- + ---------------------
2 2 7 7
$$- \frac{5 \log{\left(8 \right)}}{2} - \frac{9 \sqrt{7} \operatorname{atan}{\left(\frac{3 \sqrt{7}}{7} \right)}}{7} + 1 + \frac{5 \log{\left(4 \right)}}{2} + \frac{9 \sqrt{7} \operatorname{atan}{\left(\frac{5 \sqrt{7}}{7} \right)}}{7}$$
1 - 5*log(8)/2 + 5*log(4)/2 - 9*sqrt(7)*atan(3*sqrt(7)/7)/7 + 9*sqrt(7)*atan(5*sqrt(7)/7)/7
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.