Sr Examen
Integral de 1/(cos²3x) dx
Solución
Ha introducido
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1 / | | 1 | -------- dx | 23 | cos (x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\cos^{23}{\left(x \right)}}\, dx$$
Integral(1/(cos(x)^23), (x, 0, 1))
Respuesta (Indefinida)
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/ | 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) | /
$$\int \frac{1}{\cos^{23}{\left(x \right)}}\, dx = C - \frac{14549535 \sin^{21}{\left(x \right)} - 155195040 \sin^{19}{\left(x \right)} + 749786037 \sin^{17}{\left(x \right)} - 2163862272 \sin^{15}{\left(x \right)} + 4139920070 \sin^{13}{\left(x \right)} - 5503713280 \sin^{11}{\left(x \right)} + 5174056250 \sin^{9}{\left(x \right)} - 3424523520 \sin^{7}{\left(x \right)} + 1551313995 \sin^{5}{\left(x \right)} - 450357600 \sin^{3}{\left(x \right)} + 71957985 \sin{\left(x \right)}}{86507520 \sin^{22}{\left(x \right)} - 951582720 \sin^{20}{\left(x \right)} + 4757913600 \sin^{18}{\left(x \right)} - 14273740800 \sin^{16}{\left(x \right)} + 28547481600 \sin^{14}{\left(x \right)} - 39966474240 \sin^{12}{\left(x \right)} + 39966474240 \sin^{10}{\left(x \right)} - 28547481600 \sin^{8}{\left(x \right)} + 14273740800 \sin^{6}{\left(x \right)} - 4757913600 \sin^{4}{\left(x \right)} + 951582720 \sin^{2}{\left(x \right)} - 86507520} - \frac{88179 \log{\left(\sin{\left(x \right)} - 1 \right)}}{1048576} + \frac{88179 \log{\left(\sin{\left(x \right)} + 1 \right)}}{1048576}$$
Gráfica
Respuesta
[src]
11 7 15 3 19 21 17 5 13 9
88179*log(1 - sin(1)) 88179*log(1 + sin(1)) - 5503713280*sin (1) - 3424523520*sin (1) - 2163862272*sin (1) - 450357600*sin (1) - 155195040*sin (1) + 14549535*sin (1) + 71957985*sin(1) + 749786037*sin (1) + 1551313995*sin (1) + 4139920070*sin (1) + 5174056250*sin (1)
- --------------------- + --------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1048576 1048576 12 8 16 4 20 22 2 18 6 14 10
-86507520 - 39966474240*sin (1) - 28547481600*sin (1) - 14273740800*sin (1) - 4757913600*sin (1) - 951582720*sin (1) + 86507520*sin (1) + 951582720*sin (1) + 4757913600*sin (1) + 14273740800*sin (1) + 28547481600*sin (1) + 39966474240*sin (1)
$$\frac{88179 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{1048576} - \frac{88179 \log{\left(1 - \sin{\left(1 \right)} \right)}}{1048576} - \frac{- 3424523520 \sin^{7}{\left(1 \right)} - 5503713280 \sin^{11}{\left(1 \right)} - 450357600 \sin^{3}{\left(1 \right)} - 2163862272 \sin^{15}{\left(1 \right)} - 155195040 \sin^{19}{\left(1 \right)} + 14549535 \sin^{21}{\left(1 \right)} + 749786037 \sin^{17}{\left(1 \right)} + 71957985 \sin{\left(1 \right)} + 4139920070 \sin^{13}{\left(1 \right)} + 1551313995 \sin^{5}{\left(1 \right)} + 5174056250 \sin^{9}{\left(1 \right)}}{- 28547481600 \sin^{8}{\left(1 \right)} - 39966474240 \sin^{12}{\left(1 \right)} - 4757913600 \sin^{4}{\left(1 \right)} - 14273740800 \sin^{16}{\left(1 \right)} - 86507520 - 951582720 \sin^{20}{\left(1 \right)} + 86507520 \sin^{22}{\left(1 \right)} + 4757913600 \sin^{18}{\left(1 \right)} + 951582720 \sin^{2}{\left(1 \right)} + 28547481600 \sin^{14}{\left(1 \right)} + 14273740800 \sin^{6}{\left(1 \right)} + 39966474240 \sin^{10}{\left(1 \right)}}$$
=
=
11 7 15 3 19 21 17 5 13 9
88179*log(1 - sin(1)) 88179*log(1 + sin(1)) - 5503713280*sin (1) - 3424523520*sin (1) - 2163862272*sin (1) - 450357600*sin (1) - 155195040*sin (1) + 14549535*sin (1) + 71957985*sin(1) + 749786037*sin (1) + 1551313995*sin (1) + 4139920070*sin (1) + 5174056250*sin (1)
- --------------------- + --------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1048576 1048576 12 8 16 4 20 22 2 18 6 14 10
-86507520 - 39966474240*sin (1) - 28547481600*sin (1) - 14273740800*sin (1) - 4757913600*sin (1) - 951582720*sin (1) + 86507520*sin (1) + 951582720*sin (1) + 4757913600*sin (1) + 14273740800*sin (1) + 28547481600*sin (1) + 39966474240*sin (1)
$$\frac{88179 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{1048576} - \frac{88179 \log{\left(1 - \sin{\left(1 \right)} \right)}}{1048576} - \frac{- 3424523520 \sin^{7}{\left(1 \right)} - 5503713280 \sin^{11}{\left(1 \right)} - 450357600 \sin^{3}{\left(1 \right)} - 2163862272 \sin^{15}{\left(1 \right)} - 155195040 \sin^{19}{\left(1 \right)} + 14549535 \sin^{21}{\left(1 \right)} + 749786037 \sin^{17}{\left(1 \right)} + 71957985 \sin{\left(1 \right)} + 4139920070 \sin^{13}{\left(1 \right)} + 1551313995 \sin^{5}{\left(1 \right)} + 5174056250 \sin^{9}{\left(1 \right)}}{- 28547481600 \sin^{8}{\left(1 \right)} - 39966474240 \sin^{12}{\left(1 \right)} - 4757913600 \sin^{4}{\left(1 \right)} - 14273740800 \sin^{16}{\left(1 \right)} - 86507520 - 951582720 \sin^{20}{\left(1 \right)} + 86507520 \sin^{22}{\left(1 \right)} + 4757913600 \sin^{18}{\left(1 \right)} + 951582720 \sin^{2}{\left(1 \right)} + 28547481600 \sin^{14}{\left(1 \right)} + 14273740800 \sin^{6}{\left(1 \right)} + 39966474240 \sin^{10}{\left(1 \right)}}$$
-88179*log(1 - sin(1))/1048576 + 88179*log(1 + sin(1))/1048576 - (-5503713280*sin(1)^11 - 3424523520*sin(1)^7 - 2163862272*sin(1)^15 - 450357600*sin(1)^3 - 155195040*sin(1)^19 + 14549535*sin(1)^21 + 71957985*sin(1) + 749786037*sin(1)^17 + 1551313995*sin(1)^5 + 4139920070*sin(1)^13 + 5174056250*sin(1)^9)/(-86507520 - 39966474240*sin(1)^12 - 28547481600*sin(1)^8 - 14273740800*sin(1)^16 - 4757913600*sin(1)^4 - 951582720*sin(1)^20 + 86507520*sin(1)^22 + 951582720*sin(1)^2 + 4757913600*sin(1)^18 + 14273740800*sin(1)^6 + 28547481600*sin(1)^14 + 39966474240*sin(1)^10)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.