Sr Examen
Integral de cos^2(5x+3) dx
Solución
Ha introducido
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1 / | | 2 | cos (5*x + 3) dx | / 0
$$\int\limits_{0}^{1} \cos^{2}{\left(5 x + 3 \right)}\, dx$$
Integral(cos(5*x + 3)^2, (x, 0, 1))
Respuesta (Indefinida)
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/ 3/3 5*x\ /3 5*x\ 4/3 5*x\ 2/3 5*x\
| 2*tan |- + ---| 2*tan|- + ---| 5*x*tan |- + ---| 10*x*tan |- + ---|
| 2 \2 2 / \2 2 / 5*x \2 2 / \2 2 /
| cos (5*x + 3) dx = C - ---------------------------------------- + ---------------------------------------- + ---------------------------------------- + ---------------------------------------- + ----------------------------------------
| 4/3 5*x\ 2/3 5*x\ 4/3 5*x\ 2/3 5*x\ 4/3 5*x\ 2/3 5*x\ 4/3 5*x\ 2/3 5*x\ 4/3 5*x\ 2/3 5*x\
/ 10 + 10*tan |- + ---| + 20*tan |- + ---| 10 + 10*tan |- + ---| + 20*tan |- + ---| 10 + 10*tan |- + ---| + 20*tan |- + ---| 10 + 10*tan |- + ---| + 20*tan |- + ---| 10 + 10*tan |- + ---| + 20*tan |- + ---|
\2 2 / \2 2 / \2 2 / \2 2 / \2 2 / \2 2 / \2 2 / \2 2 / \2 2 / \2 2 /
$$\int \cos^{2}{\left(5 x + 3 \right)}\, dx = C + \frac{5 x \tan^{4}{\left(\frac{5 x}{2} + \frac{3}{2} \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 10} + \frac{10 x \tan^{2}{\left(\frac{5 x}{2} + \frac{3}{2} \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 10} + \frac{5 x}{10 \tan^{4}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 10} - \frac{2 \tan^{3}{\left(\frac{5 x}{2} + \frac{3}{2} \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 10} + \frac{2 \tan{\left(\frac{5 x}{2} + \frac{3}{2} \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} + \frac{3}{2} \right)} + 10}$$
Gráfica
Respuesta
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2 2 cos (8) sin (8) cos(3)*sin(3) cos(8)*sin(8) ------- + ------- - ------------- + ------------- 2 2 10 10
$$\frac{\sin{\left(8 \right)} \cos{\left(8 \right)}}{10} + \frac{\cos^{2}{\left(8 \right)}}{2} - \frac{\sin{\left(3 \right)} \cos{\left(3 \right)}}{10} + \frac{\sin^{2}{\left(8 \right)}}{2}$$
=
=
2 2 cos (8) sin (8) cos(3)*sin(3) cos(8)*sin(8) ------- + ------- - ------------- + ------------- 2 2 10 10
$$\frac{\sin{\left(8 \right)} \cos{\left(8 \right)}}{10} + \frac{\cos^{2}{\left(8 \right)}}{2} - \frac{\sin{\left(3 \right)} \cos{\left(3 \right)}}{10} + \frac{\sin^{2}{\left(8 \right)}}{2}$$
cos(8)^2/2 + sin(8)^2/2 - cos(3)*sin(3)/10 + cos(8)*sin(8)/10
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.