Sr Examen
Integral de dx/Cos^23x dx
Solución
Ha introducido
[src]
p - 9 / | | 1 | -------- dx | 23 | cos (x) | / 0
$$\int\limits_{0}^{\frac{p}{9}} \frac{1}{\cos^{23}{\left(x \right)}}\, dx$$
Integral(1/(cos(x)^23), (x, 0, p/9))
Respuesta (Indefinida)
[src]
/ | 11 7 15 3 19 21 17 5 13 9 | 1 88179*log(-1 + sin(x)) 88179*log(1 + sin(x)) - 5503713280*sin (x) - 3424523520*sin (x) - 2163862272*sin (x) - 450357600*sin (x) - 155195040*sin (x) + 14549535*sin (x) + 71957985*sin(x) + 749786037*sin (x) + 1551313995*sin (x) + 4139920070*sin (x) + 5174056250*sin (x) | -------- dx = C - ---------------------- + --------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 23 1048576 1048576 12 8 16 4 20 22 2 18 6 14 10 | cos (x) -86507520 - 39966474240*sin (x) - 28547481600*sin (x) - 14273740800*sin (x) - 4757913600*sin (x) - 951582720*sin (x) + 86507520*sin (x) + 951582720*sin (x) + 4757913600*sin (x) + 14273740800*sin (x) + 28547481600*sin (x) + 39966474240*sin (x) | /
$$\int \frac{1}{\cos^{23}{\left(x \right)}}\, dx = C - \frac{14549535 \sin^{21}{\left(x \right)} - 155195040 \sin^{19}{\left(x \right)} + 749786037 \sin^{17}{\left(x \right)} - 2163862272 \sin^{15}{\left(x \right)} + 4139920070 \sin^{13}{\left(x \right)} - 5503713280 \sin^{11}{\left(x \right)} + 5174056250 \sin^{9}{\left(x \right)} - 3424523520 \sin^{7}{\left(x \right)} + 1551313995 \sin^{5}{\left(x \right)} - 450357600 \sin^{3}{\left(x \right)} + 71957985 \sin{\left(x \right)}}{86507520 \sin^{22}{\left(x \right)} - 951582720 \sin^{20}{\left(x \right)} + 4757913600 \sin^{18}{\left(x \right)} - 14273740800 \sin^{16}{\left(x \right)} + 28547481600 \sin^{14}{\left(x \right)} - 39966474240 \sin^{12}{\left(x \right)} + 39966474240 \sin^{10}{\left(x \right)} - 28547481600 \sin^{8}{\left(x \right)} + 14273740800 \sin^{6}{\left(x \right)} - 4757913600 \sin^{4}{\left(x \right)} + 951582720 \sin^{2}{\left(x \right)} - 86507520} - \frac{88179 \log{\left(\sin{\left(x \right)} - 1 \right)}}{1048576} + \frac{88179 \log{\left(\sin{\left(x \right)} + 1 \right)}}{1048576}$$
Respuesta
[src]
/ /p\\ / /p\\ 11/p\ 7/p\ 15/p\ 3/p\ 19/p\ 21/p\ /p\ 17/p\ 5/p\ 13/p\ 9/p\
88179*log|-1 + sin|-|| 88179*log|1 + sin|-|| - 5503713280*sin |-| - 3424523520*sin |-| - 2163862272*sin |-| - 450357600*sin |-| - 155195040*sin |-| + 14549535*sin |-| + 71957985*sin|-| + 749786037*sin |-| + 1551313995*sin |-| + 4139920070*sin |-| + 5174056250*sin |-|
\ \9// \ \9// \9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/ 88179*pi*I
- ---------------------- + --------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------
1048576 1048576 12/p\ 8/p\ 16/p\ 4/p\ 20/p\ 22/p\ 2/p\ 18/p\ 6/p\ 14/p\ 10/p\ 1048576
-86507520 - 39966474240*sin |-| - 28547481600*sin |-| - 14273740800*sin |-| - 4757913600*sin |-| - 951582720*sin |-| + 86507520*sin |-| + 951582720*sin |-| + 4757913600*sin |-| + 14273740800*sin |-| + 28547481600*sin |-| + 39966474240*sin |-|
\9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/
$$- \frac{14549535 \sin^{21}{\left(\frac{p}{9} \right)} - 155195040 \sin^{19}{\left(\frac{p}{9} \right)} + 749786037 \sin^{17}{\left(\frac{p}{9} \right)} - 2163862272 \sin^{15}{\left(\frac{p}{9} \right)} + 4139920070 \sin^{13}{\left(\frac{p}{9} \right)} - 5503713280 \sin^{11}{\left(\frac{p}{9} \right)} + 5174056250 \sin^{9}{\left(\frac{p}{9} \right)} - 3424523520 \sin^{7}{\left(\frac{p}{9} \right)} + 1551313995 \sin^{5}{\left(\frac{p}{9} \right)} - 450357600 \sin^{3}{\left(\frac{p}{9} \right)} + 71957985 \sin{\left(\frac{p}{9} \right)}}{86507520 \sin^{22}{\left(\frac{p}{9} \right)} - 951582720 \sin^{20}{\left(\frac{p}{9} \right)} + 4757913600 \sin^{18}{\left(\frac{p}{9} \right)} - 14273740800 \sin^{16}{\left(\frac{p}{9} \right)} + 28547481600 \sin^{14}{\left(\frac{p}{9} \right)} - 39966474240 \sin^{12}{\left(\frac{p}{9} \right)} + 39966474240 \sin^{10}{\left(\frac{p}{9} \right)} - 28547481600 \sin^{8}{\left(\frac{p}{9} \right)} + 14273740800 \sin^{6}{\left(\frac{p}{9} \right)} - 4757913600 \sin^{4}{\left(\frac{p}{9} \right)} + 951582720 \sin^{2}{\left(\frac{p}{9} \right)} - 86507520} - \frac{88179 \log{\left(\sin{\left(\frac{p}{9} \right)} - 1 \right)}}{1048576} + \frac{88179 \log{\left(\sin{\left(\frac{p}{9} \right)} + 1 \right)}}{1048576} + \frac{88179 i \pi}{1048576}$$
=
=
/ /p\\ / /p\\ 11/p\ 7/p\ 15/p\ 3/p\ 19/p\ 21/p\ /p\ 17/p\ 5/p\ 13/p\ 9/p\
88179*log|-1 + sin|-|| 88179*log|1 + sin|-|| - 5503713280*sin |-| - 3424523520*sin |-| - 2163862272*sin |-| - 450357600*sin |-| - 155195040*sin |-| + 14549535*sin |-| + 71957985*sin|-| + 749786037*sin |-| + 1551313995*sin |-| + 4139920070*sin |-| + 5174056250*sin |-|
\ \9// \ \9// \9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/ 88179*pi*I
- ---------------------- + --------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------
1048576 1048576 12/p\ 8/p\ 16/p\ 4/p\ 20/p\ 22/p\ 2/p\ 18/p\ 6/p\ 14/p\ 10/p\ 1048576
-86507520 - 39966474240*sin |-| - 28547481600*sin |-| - 14273740800*sin |-| - 4757913600*sin |-| - 951582720*sin |-| + 86507520*sin |-| + 951582720*sin |-| + 4757913600*sin |-| + 14273740800*sin |-| + 28547481600*sin |-| + 39966474240*sin |-|
\9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/ \9/
$$- \frac{14549535 \sin^{21}{\left(\frac{p}{9} \right)} - 155195040 \sin^{19}{\left(\frac{p}{9} \right)} + 749786037 \sin^{17}{\left(\frac{p}{9} \right)} - 2163862272 \sin^{15}{\left(\frac{p}{9} \right)} + 4139920070 \sin^{13}{\left(\frac{p}{9} \right)} - 5503713280 \sin^{11}{\left(\frac{p}{9} \right)} + 5174056250 \sin^{9}{\left(\frac{p}{9} \right)} - 3424523520 \sin^{7}{\left(\frac{p}{9} \right)} + 1551313995 \sin^{5}{\left(\frac{p}{9} \right)} - 450357600 \sin^{3}{\left(\frac{p}{9} \right)} + 71957985 \sin{\left(\frac{p}{9} \right)}}{86507520 \sin^{22}{\left(\frac{p}{9} \right)} - 951582720 \sin^{20}{\left(\frac{p}{9} \right)} + 4757913600 \sin^{18}{\left(\frac{p}{9} \right)} - 14273740800 \sin^{16}{\left(\frac{p}{9} \right)} + 28547481600 \sin^{14}{\left(\frac{p}{9} \right)} - 39966474240 \sin^{12}{\left(\frac{p}{9} \right)} + 39966474240 \sin^{10}{\left(\frac{p}{9} \right)} - 28547481600 \sin^{8}{\left(\frac{p}{9} \right)} + 14273740800 \sin^{6}{\left(\frac{p}{9} \right)} - 4757913600 \sin^{4}{\left(\frac{p}{9} \right)} + 951582720 \sin^{2}{\left(\frac{p}{9} \right)} - 86507520} - \frac{88179 \log{\left(\sin{\left(\frac{p}{9} \right)} - 1 \right)}}{1048576} + \frac{88179 \log{\left(\sin{\left(\frac{p}{9} \right)} + 1 \right)}}{1048576} + \frac{88179 i \pi}{1048576}$$
-88179*log(-1 + sin(p/9))/1048576 + 88179*log(1 + sin(p/9))/1048576 - (-5503713280*sin(p/9)^11 - 3424523520*sin(p/9)^7 - 2163862272*sin(p/9)^15 - 450357600*sin(p/9)^3 - 155195040*sin(p/9)^19 + 14549535*sin(p/9)^21 + 71957985*sin(p/9) + 749786037*sin(p/9)^17 + 1551313995*sin(p/9)^5 + 4139920070*sin(p/9)^13 + 5174056250*sin(p/9)^9)/(-86507520 - 39966474240*sin(p/9)^12 - 28547481600*sin(p/9)^8 - 14273740800*sin(p/9)^16 - 4757913600*sin(p/9)^4 - 951582720*sin(p/9)^20 + 86507520*sin(p/9)^22 + 951582720*sin(p/9)^2 + 4757913600*sin(p/9)^18 + 14273740800*sin(p/9)^6 + 28547481600*sin(p/9)^14 + 39966474240*sin(p/9)^10) + 88179*pi*i/1048576
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.