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