Sr Examen
Integral de (3x^2-5)/cos^2(x^3-5x+10) dx
Solución
Ha introducido
[src]
1 / | | 2 | 3*x - 5 | ------------------- dx | 2/ 3 \ | cos \x - 5*x + 10/ | / 0
$$\int\limits_{0}^{1} \frac{3 x^{2} - 5}{\cos^{2}{\left(\left(x^{3} - 5 x\right) + 10 \right)}}\, dx$$
Integral((3*x^2 - 5)/cos(x^3 - 5*x + 10)^2, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / | / | | 2 | | 2 | 3*x - 5 | 1 | x | ------------------- dx = C - 5* | ------------------- dx + 3* | ------------------- dx | 2/ 3 \ | 2/ 3 \ | 2/ 3 \ | cos \x - 5*x + 10/ | cos \x - 5*x + 10/ | cos \x - 5*x + 10/ | | | / / /
$$\int \frac{3 x^{2} - 5}{\cos^{2}{\left(\left(x^{3} - 5 x\right) + 10 \right)}}\, dx = C + 3 \int \frac{x^{2}}{\cos^{2}{\left(\left(x^{3} - 5 x\right) + 10 \right)}}\, dx - 5 \int \frac{1}{\cos^{2}{\left(\left(x^{3} - 5 x\right) + 10 \right)}}\, dx$$
Gráfica
Respuesta
[src]
2*tan(3) 2*tan(5)
- ------------ + ------------
2 2
-1 + tan (3) -1 + tan (5)
$$\frac{2 \tan{\left(5 \right)}}{-1 + \tan^{2}{\left(5 \right)}} - \frac{2 \tan{\left(3 \right)}}{-1 + \tan^{2}{\left(3 \right)}}$$
=
=
2*tan(3) 2*tan(5)
- ------------ + ------------
2 2
-1 + tan (3) -1 + tan (5)
$$\frac{2 \tan{\left(5 \right)}}{-1 + \tan^{2}{\left(5 \right)}} - \frac{2 \tan{\left(3 \right)}}{-1 + \tan^{2}{\left(3 \right)}}$$
-2*tan(3)/(-1 + tan(3)^2) + 2*tan(5)/(-1 + tan(5)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.