Sr Examen
Integral de (tanx)^4(secx)^7dx dx
Solución
Ha introducido
[src]
1 / | | 4 7 | tan (x)*sec (x) dx | / 0
$$\int\limits_{0}^{1} \tan^{4}{\left(x \right)} \sec^{7}{\left(x \right)}\, dx$$
Integral(tan(x)^4*sec(x)^7, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 7 9 3 5 | 4 7 3*log(-1 + sin(x)) 3*log(1 + sin(x)) - 70*sin (x) - 15*sin(x) + 15*sin (x) + 70*sin (x) + 128*sin (x) | tan (x)*sec (x) dx = C - ------------------ + ----------------- - ----------------------------------------------------------------------------------- | 512 512 4 8 10 2 6 / -1280 - 12800*sin (x) - 6400*sin (x) + 1280*sin (x) + 6400*sin (x) + 12800*sin (x)
$$\int \tan^{4}{\left(x \right)} \sec^{7}{\left(x \right)}\, dx = C - \frac{15 \sin^{9}{\left(x \right)} - 70 \sin^{7}{\left(x \right)} + 128 \sin^{5}{\left(x \right)} + 70 \sin^{3}{\left(x \right)} - 15 \sin{\left(x \right)}}{1280 \sin^{10}{\left(x \right)} - 6400 \sin^{8}{\left(x \right)} + 12800 \sin^{6}{\left(x \right)} - 12800 \sin^{4}{\left(x \right)} + 6400 \sin^{2}{\left(x \right)} - 1280} - \frac{3 \log{\left(\sin{\left(x \right)} - 1 \right)}}{512} + \frac{3 \log{\left(\sin{\left(x \right)} + 1 \right)}}{512}$$
Gráfica
Respuesta
[src]
7 9 3 5
3*log(1 - sin(1)) 3*log(1 + sin(1)) - 70*sin (1) - 15*sin(1) + 15*sin (1) + 70*sin (1) + 128*sin (1)
- ----------------- + ----------------- - -----------------------------------------------------------------------------------
512 512 4 8 10 2 6
-1280 - 12800*sin (1) - 6400*sin (1) + 1280*sin (1) + 6400*sin (1) + 12800*sin (1)
$$\frac{3 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{512} - \frac{3 \log{\left(1 - \sin{\left(1 \right)} \right)}}{512} - \frac{- 70 \sin^{7}{\left(1 \right)} - 15 \sin{\left(1 \right)} + 15 \sin^{9}{\left(1 \right)} + 70 \sin^{3}{\left(1 \right)} + 128 \sin^{5}{\left(1 \right)}}{- 12800 \sin^{4}{\left(1 \right)} - 6400 \sin^{8}{\left(1 \right)} - 1280 + 1280 \sin^{10}{\left(1 \right)} + 6400 \sin^{2}{\left(1 \right)} + 12800 \sin^{6}{\left(1 \right)}}$$
=
=
7 9 3 5
3*log(1 - sin(1)) 3*log(1 + sin(1)) - 70*sin (1) - 15*sin(1) + 15*sin (1) + 70*sin (1) + 128*sin (1)
- ----------------- + ----------------- - -----------------------------------------------------------------------------------
512 512 4 8 10 2 6
-1280 - 12800*sin (1) - 6400*sin (1) + 1280*sin (1) + 6400*sin (1) + 12800*sin (1)
$$\frac{3 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{512} - \frac{3 \log{\left(1 - \sin{\left(1 \right)} \right)}}{512} - \frac{- 70 \sin^{7}{\left(1 \right)} - 15 \sin{\left(1 \right)} + 15 \sin^{9}{\left(1 \right)} + 70 \sin^{3}{\left(1 \right)} + 128 \sin^{5}{\left(1 \right)}}{- 12800 \sin^{4}{\left(1 \right)} - 6400 \sin^{8}{\left(1 \right)} - 1280 + 1280 \sin^{10}{\left(1 \right)} + 6400 \sin^{2}{\left(1 \right)} + 12800 \sin^{6}{\left(1 \right)}}$$
-3*log(1 - sin(1))/512 + 3*log(1 + sin(1))/512 - (-70*sin(1)^7 - 15*sin(1) + 15*sin(1)^9 + 70*sin(1)^3 + 128*sin(1)^5)/(-1280 - 12800*sin(1)^4 - 6400*sin(1)^8 + 1280*sin(1)^10 + 6400*sin(1)^2 + 12800*sin(1)^6)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.