Sr Examen
Integral de sin^2(5x-2) dx
Solución
Ha introducido
[src]
1 / | | 2 | sin (5*x - 2) dx | / 0
$$\int\limits_{0}^{1} \sin^{2}{\left(5 x - 2 \right)}\, dx$$
Integral(sin(5*x - 2)^2, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / 5*x\ 3/ 5*x\ 4/ 5*x\ 2/ 5*x\
| 2*tan|-1 + ---| 2*tan |-1 + ---| 5*x*tan |-1 + ---| 10*x*tan |-1 + ---|
| 2 \ 2 / \ 2 / 5*x \ 2 / \ 2 /
| sin (5*x - 2) dx = C - ------------------------------------------ + ------------------------------------------ + ------------------------------------------ + ------------------------------------------ + ------------------------------------------
| 4/ 5*x\ 2/ 5*x\ 4/ 5*x\ 2/ 5*x\ 4/ 5*x\ 2/ 5*x\ 4/ 5*x\ 2/ 5*x\ 4/ 5*x\ 2/ 5*x\
/ 10 + 10*tan |-1 + ---| + 20*tan |-1 + ---| 10 + 10*tan |-1 + ---| + 20*tan |-1 + ---| 10 + 10*tan |-1 + ---| + 20*tan |-1 + ---| 10 + 10*tan |-1 + ---| + 20*tan |-1 + ---| 10 + 10*tan |-1 + ---| + 20*tan |-1 + ---|
\ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 /
$$\int \sin^{2}{\left(5 x - 2 \right)}\, dx = C + \frac{5 x \tan^{4}{\left(\frac{5 x}{2} - 1 \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} - 1 \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} - 1 \right)} + 10} + \frac{10 x \tan^{2}{\left(\frac{5 x}{2} - 1 \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} - 1 \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} - 1 \right)} + 10} + \frac{5 x}{10 \tan^{4}{\left(\frac{5 x}{2} - 1 \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} - 1 \right)} + 10} + \frac{2 \tan^{3}{\left(\frac{5 x}{2} - 1 \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} - 1 \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} - 1 \right)} + 10} - \frac{2 \tan{\left(\frac{5 x}{2} - 1 \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} - 1 \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} - 1 \right)} + 10}$$
Gráfica
Respuesta
[src]
2 2 cos (3) sin (3) cos(2)*sin(2) cos(3)*sin(3) ------- + ------- - ------------- - ------------- 2 2 10 10
$$\frac{\sin^{2}{\left(3 \right)}}{2} - \frac{\sin{\left(3 \right)} \cos{\left(3 \right)}}{10} - \frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{10} + \frac{\cos^{2}{\left(3 \right)}}{2}$$
=
=
2 2 cos (3) sin (3) cos(2)*sin(2) cos(3)*sin(3) ------- + ------- - ------------- - ------------- 2 2 10 10
$$\frac{\sin^{2}{\left(3 \right)}}{2} - \frac{\sin{\left(3 \right)} \cos{\left(3 \right)}}{10} - \frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{10} + \frac{\cos^{2}{\left(3 \right)}}{2}$$
cos(3)^2/2 + sin(3)^2/2 - cos(2)*sin(2)/10 - cos(3)*sin(3)/10
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.