Sr Examen
Integral de (1-cos^2(x))/cos^4(x) dx
Solución
Ha introducido
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1 / | | 2 | 1 - cos (x) | ----------- dx | 4 | cos (x) | / 0
$$\int\limits_{0}^{1} \frac{1 - \cos^{2}{\left(x \right)}}{\cos^{4}{\left(x \right)}}\, dx$$
Integral((1 - cos(x)^2)/cos(x)^4, (x, 0, 1))
Respuesta (Indefinida)
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/ | | 2 3 | 1 - cos (x) tan (x) sin(x) | ----------- dx = C + ------- - ------ + tan(x) | 4 3 cos(x) | cos (x) | /
$$\int \frac{1 - \cos^{2}{\left(x \right)}}{\cos^{4}{\left(x \right)}}\, dx = C - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\tan^{3}{\left(x \right)}}{3} + \tan{\left(x \right)}$$
Gráfica
Respuesta
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3
-8*tan (1/2)
--------------------------------------------
4 6 2
-3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)
$$- \frac{8 \tan^{3}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}}$$
=
=
3
-8*tan (1/2)
--------------------------------------------
4 6 2
-3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)
$$- \frac{8 \tan^{3}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}}$$
-8*tan(1/2)^3/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.