Sr Examen
Integral de 1/(4+(5sinx^2)-(8cosx^2)) dx
Solución
Ha introducido
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1 / | | 1 | ------------------------- dx | 2 2 | 4 + 5*sin (x) - 8*cos (x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(5 \sin^{2}{\left(x \right)} + 4\right) - 8 \cos^{2}{\left(x \right)}}\, dx$$
Integral(1/(4 + 5*sin(x)^2 - 8*cos(x)^2), (x, 0, 1))
Respuesta (Indefinida)
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/ / 2/x\ /x\\ / 2/x\ /x\\ | log|-1 + tan |-| - 3*tan|-|| log|-1 + tan |-| + 3*tan|-|| | 1 \ \2/ \2// \ \2/ \2// | ------------------------- dx = C - ---------------------------- + ---------------------------- | 2 2 12 12 | 4 + 5*sin (x) - 8*cos (x) | /
$$\int \frac{1}{\left(5 \sin^{2}{\left(x \right)} + 4\right) - 8 \cos^{2}{\left(x \right)}}\, dx = C - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 3 \tan{\left(\frac{x}{2} \right)} - 1 \right)}}{12} + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 3 \tan{\left(\frac{x}{2} \right)} - 1 \right)}}{12}$$
Gráfica
Respuesta
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/ 2 \ / 2 \
log\1 - tan (1/2) + 3*tan(1/2)/ log\-1 + tan (1/2) + 3*tan(1/2)/ pi*I
- ------------------------------- + -------------------------------- - ----
12 12 12
$$- \frac{\log{\left(- \tan^{2}{\left(\frac{1}{2} \right)} + 1 + 3 \tan{\left(\frac{1}{2} \right)} \right)}}{12} + \frac{\log{\left(-1 + \tan^{2}{\left(\frac{1}{2} \right)} + 3 \tan{\left(\frac{1}{2} \right)} \right)}}{12} - \frac{i \pi}{12}$$
=
=
/ 2 \ / 2 \
log\1 - tan (1/2) + 3*tan(1/2)/ log\-1 + tan (1/2) + 3*tan(1/2)/ pi*I
- ------------------------------- + -------------------------------- - ----
12 12 12
$$- \frac{\log{\left(- \tan^{2}{\left(\frac{1}{2} \right)} + 1 + 3 \tan{\left(\frac{1}{2} \right)} \right)}}{12} + \frac{\log{\left(-1 + \tan^{2}{\left(\frac{1}{2} \right)} + 3 \tan{\left(\frac{1}{2} \right)} \right)}}{12} - \frac{i \pi}{12}$$
-log(1 - tan(1/2)^2 + 3*tan(1/2))/12 + log(-1 + tan(1/2)^2 + 3*tan(1/2))/12 - pi*i/12
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.