Sr Examen
Integral de tan(x)^4sec(x)^5 dx
Solución
Ha introducido
[src]
1 / | | 4 5 | tan (x)*sec (x) dx | / 0
$$\int\limits_{0}^{1} \tan^{4}{\left(x \right)} \sec^{5}{\left(x \right)}\, dx$$
Integral(tan(x)^4*sec(x)^5, (x, 0, 1))
Respuesta (Indefinida)
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/ | 3 5 7 | 4 5 3*log(-1 + sin(x)) 3*log(1 + sin(x)) - 11*sin (x) - 11*sin (x) + 3*sin (x) + 3*sin(x) | tan (x)*sec (x) dx = C - ------------------ + ----------------- - ----------------------------------------------------------- | 256 256 2 6 8 4 / 128 - 512*sin (x) - 512*sin (x) + 128*sin (x) + 768*sin (x)
$$\int \tan^{4}{\left(x \right)} \sec^{5}{\left(x \right)}\, dx = C - \frac{3 \sin^{7}{\left(x \right)} - 11 \sin^{5}{\left(x \right)} - 11 \sin^{3}{\left(x \right)} + 3 \sin{\left(x \right)}}{128 \sin^{8}{\left(x \right)} - 512 \sin^{6}{\left(x \right)} + 768 \sin^{4}{\left(x \right)} - 512 \sin^{2}{\left(x \right)} + 128} - \frac{3 \log{\left(\sin{\left(x \right)} - 1 \right)}}{256} + \frac{3 \log{\left(\sin{\left(x \right)} + 1 \right)}}{256}$$
Gráfica
Respuesta
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3 5 7
3*log(1 - sin(1)) 3*log(1 + sin(1)) - 11*sin (1) - 11*sin (1) + 3*sin (1) + 3*sin(1)
- ----------------- + ----------------- - -----------------------------------------------------------
256 256 2 6 8 4
128 - 512*sin (1) - 512*sin (1) + 128*sin (1) + 768*sin (1)
$$\frac{3 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{256} - \frac{3 \log{\left(1 - \sin{\left(1 \right)} \right)}}{256} - \frac{- 11 \sin^{3}{\left(1 \right)} - 11 \sin^{5}{\left(1 \right)} + 3 \sin^{7}{\left(1 \right)} + 3 \sin{\left(1 \right)}}{- 512 \sin^{2}{\left(1 \right)} - 512 \sin^{6}{\left(1 \right)} + 128 \sin^{8}{\left(1 \right)} + 128 + 768 \sin^{4}{\left(1 \right)}}$$
=
=
3 5 7
3*log(1 - sin(1)) 3*log(1 + sin(1)) - 11*sin (1) - 11*sin (1) + 3*sin (1) + 3*sin(1)
- ----------------- + ----------------- - -----------------------------------------------------------
256 256 2 6 8 4
128 - 512*sin (1) - 512*sin (1) + 128*sin (1) + 768*sin (1)
$$\frac{3 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{256} - \frac{3 \log{\left(1 - \sin{\left(1 \right)} \right)}}{256} - \frac{- 11 \sin^{3}{\left(1 \right)} - 11 \sin^{5}{\left(1 \right)} + 3 \sin^{7}{\left(1 \right)} + 3 \sin{\left(1 \right)}}{- 512 \sin^{2}{\left(1 \right)} - 512 \sin^{6}{\left(1 \right)} + 128 \sin^{8}{\left(1 \right)} + 128 + 768 \sin^{4}{\left(1 \right)}}$$
-3*log(1 - sin(1))/256 + 3*log(1 + sin(1))/256 - (-11*sin(1)^3 - 11*sin(1)^5 + 3*sin(1)^7 + 3*sin(1))/(128 - 512*sin(1)^2 - 512*sin(1)^6 + 128*sin(1)^8 + 768*sin(1)^4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.