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