Sr Examen
Integral de cos(x)\(sin^2(x)*cos(x)*(5cos^3(x))) dx
Solución
Ha introducido
[src]
1 / | | cos(x) | ------------------------ dx | 2 3 | sin (x)*cos(x)*5*cos (x) | / 0
$$\int\limits_{0}^{1} \frac{\cos{\left(x \right)}}{\sin^{2}{\left(x \right)} \cos{\left(x \right)} 5 \cos^{3}{\left(x \right)}}\, dx$$
Integral(cos(x)/(((sin(x)^2*cos(x))*(5*cos(x)^3))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 6/x\ 2/x\ 4/x\ 3/x\ / /x\\ 5/x\ / /x\\ / /x\\ /x\ 5/x\ / /x\\ / /x\\ /x\ 3/x\ / /x\\ | tan |-| 3*tan |-| 3*tan |-| 6*tan |-|*log|1 + tan|-|| 3*tan |-|*log|-1 + tan|-|| 3*log|-1 + tan|-||*tan|-| 3*tan |-|*log|1 + tan|-|| 3*log|1 + tan|-||*tan|-| 6*tan |-|*log|-1 + tan|-|| | cos(x) 1 \2/ \2/ \2/ \2/ \ \2// \2/ \ \2// \ \2// \2/ \2/ \ \2// \ \2// \2/ \2/ \ \2// | ------------------------ dx = C - ------------------------------------- - ------------------------------------- + ------------------------------------- + ------------------------------------- - ------------------------------------- - ------------------------------------- - ------------------------------------- + ------------------------------------- + ------------------------------------- + ------------------------------------- | 2 3 3/x\ 5/x\ /x\ 3/x\ 5/x\ /x\ 3/x\ 5/x\ /x\ 3/x\ 5/x\ /x\ 3/x\ 5/x\ /x\ 3/x\ 5/x\ /x\ 3/x\ 5/x\ /x\ 3/x\ 5/x\ /x\ 3/x\ 5/x\ /x\ 3/x\ 5/x\ /x\ | sin (x)*cos(x)*5*cos (x) - 20*tan |-| + 10*tan |-| + 10*tan|-| - 20*tan |-| + 10*tan |-| + 10*tan|-| - 20*tan |-| + 10*tan |-| + 10*tan|-| - 20*tan |-| + 10*tan |-| + 10*tan|-| - 20*tan |-| + 10*tan |-| + 10*tan|-| - 20*tan |-| + 10*tan |-| + 10*tan|-| - 20*tan |-| + 10*tan |-| + 10*tan|-| - 20*tan |-| + 10*tan |-| + 10*tan|-| - 20*tan |-| + 10*tan |-| + 10*tan|-| - 20*tan |-| + 10*tan |-| + 10*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{\cos{\left(x \right)}}{\sin^{2}{\left(x \right)} \cos{\left(x \right)} 5 \cos^{3}{\left(x \right)}}\, dx = C - \frac{3 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{5}{\left(\frac{x}{2} \right)}}{10 \tan^{5}{\left(\frac{x}{2} \right)} - 20 \tan^{3}{\left(\frac{x}{2} \right)} + 10 \tan{\left(\frac{x}{2} \right)}} + \frac{6 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{10 \tan^{5}{\left(\frac{x}{2} \right)} - 20 \tan^{3}{\left(\frac{x}{2} \right)} + 10 \tan{\left(\frac{x}{2} \right)}} - \frac{3 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan{\left(\frac{x}{2} \right)}}{10 \tan^{5}{\left(\frac{x}{2} \right)} - 20 \tan^{3}{\left(\frac{x}{2} \right)} + 10 \tan{\left(\frac{x}{2} \right)}} + \frac{3 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{5}{\left(\frac{x}{2} \right)}}{10 \tan^{5}{\left(\frac{x}{2} \right)} - 20 \tan^{3}{\left(\frac{x}{2} \right)} + 10 \tan{\left(\frac{x}{2} \right)}} - \frac{6 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{10 \tan^{5}{\left(\frac{x}{2} \right)} - 20 \tan^{3}{\left(\frac{x}{2} \right)} + 10 \tan{\left(\frac{x}{2} \right)}} + \frac{3 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan{\left(\frac{x}{2} \right)}}{10 \tan^{5}{\left(\frac{x}{2} \right)} - 20 \tan^{3}{\left(\frac{x}{2} \right)} + 10 \tan{\left(\frac{x}{2} \right)}} - \frac{\tan^{6}{\left(\frac{x}{2} \right)}}{10 \tan^{5}{\left(\frac{x}{2} \right)} - 20 \tan^{3}{\left(\frac{x}{2} \right)} + 10 \tan{\left(\frac{x}{2} \right)}} + \frac{3 \tan^{4}{\left(\frac{x}{2} \right)}}{10 \tan^{5}{\left(\frac{x}{2} \right)} - 20 \tan^{3}{\left(\frac{x}{2} \right)} + 10 \tan{\left(\frac{x}{2} \right)}} + \frac{3 \tan^{2}{\left(\frac{x}{2} \right)}}{10 \tan^{5}{\left(\frac{x}{2} \right)} - 20 \tan^{3}{\left(\frac{x}{2} \right)} + 10 \tan{\left(\frac{x}{2} \right)}} - \frac{1}{10 \tan^{5}{\left(\frac{x}{2} \right)} - 20 \tan^{3}{\left(\frac{x}{2} \right)} + 10 \tan{\left(\frac{x}{2} \right)}}$$
Gráfica
Respuesta
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3*pi*I
oo - ------
20
$$\infty - \frac{3 i \pi}{20}$$
=
=
3*pi*I
oo - ------
20
$$\infty - \frac{3 i \pi}{20}$$
oo - 3*pi*i/20
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.