Sr Examen
Integral de (2cos(x)+3sin(x))/(2sin(x)-3cos(x))^3 dx
Solución
Ha introducido
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pi -- 4 / | | 2*cos(x) + 3*sin(x) | ---------------------- dx | 3 | (2*sin(x) - 3*cos(x)) | / 0
$$\int\limits_{0}^{\frac{\pi}{4}} \frac{3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}}{\left(2 \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right)^{3}}\, dx$$
Integral((2*cos(x) + 3*sin(x))/(2*sin(x) - 3*cos(x))^3, (x, 0, pi/4))
Respuesta (Indefinida)
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/ /x\ 2/x\ 2/x\ 3/x\ | 12*tan|-| 6*tan |-| 8*tan |-| 12*tan |-| | 2*cos(x) + 3*sin(x) \2/ \2/ \2/ \2/ | ---------------------- dx = C - ------------------------------------------------------- - ---------------------------------------------------- + ------------------------------------------------------- + ------------------------------------------------------- | 3 /x\ 2/x\ 4/x\ 3/x\ /x\ 2/x\ 4/x\ 3/x\ /x\ 2/x\ 4/x\ 3/x\ /x\ 2/x\ 4/x\ 3/x\ | (2*sin(x) - 3*cos(x)) 81 - 216*tan|-| - 18*tan |-| + 81*tan |-| + 216*tan |-| 27 - 72*tan|-| - 6*tan |-| + 27*tan |-| + 72*tan |-| 81 - 216*tan|-| - 18*tan |-| + 81*tan |-| + 216*tan |-| 81 - 216*tan|-| - 18*tan |-| + 81*tan |-| + 216*tan |-| | \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ /
$$\int \frac{3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}}{\left(2 \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right)^{3}}\, dx = C + \frac{12 \tan^{3}{\left(\frac{x}{2} \right)}}{81 \tan^{4}{\left(\frac{x}{2} \right)} + 216 \tan^{3}{\left(\frac{x}{2} \right)} - 18 \tan^{2}{\left(\frac{x}{2} \right)} - 216 \tan{\left(\frac{x}{2} \right)} + 81} + \frac{8 \tan^{2}{\left(\frac{x}{2} \right)}}{81 \tan^{4}{\left(\frac{x}{2} \right)} + 216 \tan^{3}{\left(\frac{x}{2} \right)} - 18 \tan^{2}{\left(\frac{x}{2} \right)} - 216 \tan{\left(\frac{x}{2} \right)} + 81} - \frac{12 \tan{\left(\frac{x}{2} \right)}}{81 \tan^{4}{\left(\frac{x}{2} \right)} + 216 \tan^{3}{\left(\frac{x}{2} \right)} - 18 \tan^{2}{\left(\frac{x}{2} \right)} - 216 \tan{\left(\frac{x}{2} \right)} + 81} - \frac{6 \tan^{2}{\left(\frac{x}{2} \right)}}{27 \tan^{4}{\left(\frac{x}{2} \right)} + 72 \tan^{3}{\left(\frac{x}{2} \right)} - 6 \tan^{2}{\left(\frac{x}{2} \right)} - 72 \tan{\left(\frac{x}{2} \right)} + 27}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.