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