Sr Examen
Integral de (4x-10)/((x+2)(x²-2x+10)) dx
Solución
Ha introducido
[src]
1 / | | 4*x - 10 | ----------------------- dx | / 2 \ | (x + 2)*\x - 2*x + 10/ | / 0
$$\int\limits_{0}^{1} \frac{4 x - 10}{\left(x + 2\right) \left(\left(x^{2} - 2 x\right) + 10\right)}\, dx$$
Integral((4*x - 10)/(((x + 2)*(x^2 - 2*x + 10))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / 1 x\ | / 2 \ atan|- - + -| | 4*x - 10 log\10 + x - 2*x/ \ 3 3/ | ----------------------- dx = C + ------------------ - log(2 + x) + ------------- | / 2 \ 2 3 | (x + 2)*\x - 2*x + 10/ | /
$$\int \frac{4 x - 10}{\left(x + 2\right) \left(\left(x^{2} - 2 x\right) + 10\right)}\, dx = C - \log{\left(x + 2 \right)} + \frac{\log{\left(x^{2} - 2 x + 10 \right)}}{2} + \frac{\operatorname{atan}{\left(\frac{x}{3} - \frac{1}{3} \right)}}{3}$$
Gráfica
Respuesta
[src]
log(9) log(10) atan(1/3) ------ - log(3) - ------- + --------- + log(2) 2 2 3
$$- \frac{\log{\left(10 \right)}}{2} - \log{\left(3 \right)} + \frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{3} + \log{\left(2 \right)} + \frac{\log{\left(9 \right)}}{2}$$
=
=
log(9) log(10) atan(1/3) ------ - log(3) - ------- + --------- + log(2) 2 2 3
$$- \frac{\log{\left(10 \right)}}{2} - \log{\left(3 \right)} + \frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{3} + \log{\left(2 \right)} + \frac{\log{\left(9 \right)}}{2}$$
log(9)/2 - log(3) - log(10)/2 + atan(1/3)/3 + log(2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.