Sr Examen
Integral de x/(sin^4(x)cos^2(x)) dx
Solución
Ha introducido
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1 / | | x | --------------- dx | 4 2 | sin (x)*cos (x) | / 0
$$\int\limits_{0}^{1} \frac{x}{\sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}\, dx$$
Integral(x/((sin(x)^4*cos(x)^2)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x\ 7/x\ 8/x\ 4/x\ 5/x\ / 2/x\\ 3/x\ / /x\\ 3/x\ / /x\\ 3/x\ / /x\\ 2/x\ 6/x\ 5/x\ / /x\\ 5/x\ / /x\\ 5/x\ / /x\\ 3/x\ / 2/x\\ | tan|-| tan |-| x*tan |-| 90*x*tan |-| 64*tan |-|*log|1 + tan |-|| 40*tan |-|*log|tan|-|| 24*tan |-|*log|1 + tan|-|| 24*tan |-|*log|-1 + tan|-|| 20*x*tan |-| 20*x*tan |-| 24*tan |-|*log|1 + tan|-|| 24*tan |-|*log|-1 + tan|-|| 40*tan |-|*log|tan|-|| 64*tan |-|*log|1 + tan |-|| | x x \2/ \2/ \2/ \2/ \2/ \ \2// \2/ \ \2// \2/ \ \2// \2/ \ \2// \2/ \2/ \2/ \ \2// \2/ \ \2// \2/ \ \2// \2/ \ \2// | --------------- dx = C + ------------------------- + ------------------------- - ------------------------- + ------------------------- - ------------------------- - --------------------------- - ------------------------- - -------------------------- - --------------------------- + ------------------------- + ------------------------- + -------------------------- + --------------------------- + ------------------------- + --------------------------- | 4 2 3/x\ 5/x\ 3/x\ 5/x\ 3/x\ 5/x\ 3/x\ 5/x\ 3/x\ 5/x\ 3/x\ 5/x\ 3/x\ 5/x\ 3/x\ 5/x\ 3/x\ 5/x\ 3/x\ 5/x\ 3/x\ 5/x\ 3/x\ 5/x\ 3/x\ 5/x\ 3/x\ 5/x\ 3/x\ 5/x\ | sin (x)*cos (x) - 24*tan |-| + 24*tan |-| - 24*tan |-| + 24*tan |-| - 24*tan |-| + 24*tan |-| - 24*tan |-| + 24*tan |-| - 24*tan |-| + 24*tan |-| - 24*tan |-| + 24*tan |-| - 24*tan |-| + 24*tan |-| - 24*tan |-| + 24*tan |-| - 24*tan |-| + 24*tan |-| - 24*tan |-| + 24*tan |-| - 24*tan |-| + 24*tan |-| - 24*tan |-| + 24*tan |-| - 24*tan |-| + 24*tan |-| - 24*tan |-| + 24*tan |-| - 24*tan |-| + 24*tan |-| | \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ /
$$\int \frac{x}{\sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}\, dx = C + \frac{x \tan^{8}{\left(\frac{x}{2} \right)}}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}} + \frac{20 x \tan^{6}{\left(\frac{x}{2} \right)}}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}} - \frac{90 x \tan^{4}{\left(\frac{x}{2} \right)}}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}} + \frac{20 x \tan^{2}{\left(\frac{x}{2} \right)}}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}} + \frac{x}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}} + \frac{24 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{5}{\left(\frac{x}{2} \right)}}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}} - \frac{24 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}} + \frac{24 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{5}{\left(\frac{x}{2} \right)}}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}} - \frac{24 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}} - \frac{64 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{5}{\left(\frac{x}{2} \right)}}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}} + \frac{64 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}} + \frac{40 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} \tan^{5}{\left(\frac{x}{2} \right)}}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}} - \frac{40 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}} - \frac{\tan^{7}{\left(\frac{x}{2} \right)}}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}} + \frac{\tan{\left(\frac{x}{2} \right)}}{24 \tan^{5}{\left(\frac{x}{2} \right)} - 24 \tan^{3}{\left(\frac{x}{2} \right)}}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.