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