Sr Examen
Integral de (3tgx-1)/(sinx^2+4cosx^2) dx
Solución
Ha introducido
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1 / | | 3*tan(x) - 1 | ------------------- dx | 2 2 | sin (x) + 4*cos (x) | / 0
$$\int\limits_{0}^{1} \frac{3 \tan{\left(x \right)} - 1}{\sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}}\, dx$$
Integral((3*tan(x) - 1)/(sin(x)^2 + 4*cos(x)^2), (x, 0, 1))
Respuesta (Indefinida)
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/ / / ___ /x\\ / ___ /x\\ /x pi\ | | atan|\/ 3 + 2*tan|-|| atan|- \/ 3 + 2*tan|-|| |- - --| | 3*tan(x) - 1 | tan(x) \ \2// \ \2// |2 2 | | ------------------- dx = C + 3* | ------------------- dx - ---------------------- - ------------------------ - pi*floor|------| | 2 2 | 2 2 2 2 \ pi / | sin (x) + 4*cos (x) | sin (x) + 4*cos (x) | | / /
$$\int \frac{3 \tan{\left(x \right)} - 1}{\sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}}\, dx = C - \frac{\operatorname{atan}{\left(2 \tan{\left(\frac{x}{2} \right)} - \sqrt{3} \right)}}{2} - \frac{\operatorname{atan}{\left(2 \tan{\left(\frac{x}{2} \right)} + \sqrt{3} \right)}}{2} - \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor + 3 \int \frac{\tan{\left(x \right)}}{\sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}}\, dx$$
Respuesta
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1 / | | -1 + 3*tan(x) | ------------------- dx | 2 2 | sin (x) + 4*cos (x) | / 0
$$\int\limits_{0}^{1} \frac{3 \tan{\left(x \right)} - 1}{\sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}}\, dx$$
=
=
1 / | | -1 + 3*tan(x) | ------------------- dx | 2 2 | sin (x) + 4*cos (x) | / 0
$$\int\limits_{0}^{1} \frac{3 \tan{\left(x \right)} - 1}{\sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}}\, dx$$
Integral((-1 + 3*tan(x))/(sin(x)^2 + 4*cos(x)^2), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.