Sr Examen
Integral de cos((5x-1)/4)^(4) dx
Solución
Ha introducido
[src]
1 / | | 4/5*x - 1\ | cos |-------| dx | \ 4 / | / 0
$$\int\limits_{0}^{1} \cos^{4}{\left(\frac{5 x - 1}{4} \right)}\, dx$$
Integral(cos((5*x - 1)/4)^4, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 7/ 1 5*x\ 3/ 1 5*x\ 5/ 1 5*x\ / 1 5*x\ 8/ 1 5*x\ 2/ 1 5*x\ 6/ 1 5*x\ 4/ 1 5*x\ | 40*tan |- - + ---| 24*tan |- - + ---| 24*tan |- - + ---| 40*tan|- - + ---| 15*x*tan |- - + ---| 60*x*tan |- - + ---| 60*x*tan |- - + ---| 90*x*tan |- - + ---| | 4/5*x - 1\ \ 8 8 / \ 8 8 / 15*x \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / | cos |-------| dx = C - ----------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------- | \ 4 / 8/ 1 5*x\ 2/ 1 5*x\ 6/ 1 5*x\ 4/ 1 5*x\ 8/ 1 5*x\ 2/ 1 5*x\ 6/ 1 5*x\ 4/ 1 5*x\ 8/ 1 5*x\ 2/ 1 5*x\ 6/ 1 5*x\ 4/ 1 5*x\ 8/ 1 5*x\ 2/ 1 5*x\ 6/ 1 5*x\ 4/ 1 5*x\ 8/ 1 5*x\ 2/ 1 5*x\ 6/ 1 5*x\ 4/ 1 5*x\ 8/ 1 5*x\ 2/ 1 5*x\ 6/ 1 5*x\ 4/ 1 5*x\ 8/ 1 5*x\ 2/ 1 5*x\ 6/ 1 5*x\ 4/ 1 5*x\ 8/ 1 5*x\ 2/ 1 5*x\ 6/ 1 5*x\ 4/ 1 5*x\ 8/ 1 5*x\ 2/ 1 5*x\ 6/ 1 5*x\ 4/ 1 5*x\ | 40 + 40*tan |- - + ---| + 160*tan |- - + ---| + 160*tan |- - + ---| + 240*tan |- - + ---| 40 + 40*tan |- - + ---| + 160*tan |- - + ---| + 160*tan |- - + ---| + 240*tan |- - + ---| 40 + 40*tan |- - + ---| + 160*tan |- - + ---| + 160*tan |- - + ---| + 240*tan |- - + ---| 40 + 40*tan |- - + ---| + 160*tan |- - + ---| + 160*tan |- - + ---| + 240*tan |- - + ---| 40 + 40*tan |- - + ---| + 160*tan |- - + ---| + 160*tan |- - + ---| + 240*tan |- - + ---| 40 + 40*tan |- - + ---| + 160*tan |- - + ---| + 160*tan |- - + ---| + 240*tan |- - + ---| 40 + 40*tan |- - + ---| + 160*tan |- - + ---| + 160*tan |- - + ---| + 240*tan |- - + ---| 40 + 40*tan |- - + ---| + 160*tan |- - + ---| + 160*tan |- - + ---| + 240*tan |- - + ---| 40 + 40*tan |- - + ---| + 160*tan |- - + ---| + 160*tan |- - + ---| + 240*tan |- - + ---| / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 / \ 8 8 /
$$\int \cos^{4}{\left(\frac{5 x - 1}{4} \right)}\, dx = C + \frac{15 x \tan^{8}{\left(\frac{5 x}{8} - \frac{1}{8} \right)}}{40 \tan^{8}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{6}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 240 \tan^{4}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{2}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 40} + \frac{60 x \tan^{6}{\left(\frac{5 x}{8} - \frac{1}{8} \right)}}{40 \tan^{8}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{6}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 240 \tan^{4}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{2}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 40} + \frac{90 x \tan^{4}{\left(\frac{5 x}{8} - \frac{1}{8} \right)}}{40 \tan^{8}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{6}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 240 \tan^{4}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{2}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 40} + \frac{60 x \tan^{2}{\left(\frac{5 x}{8} - \frac{1}{8} \right)}}{40 \tan^{8}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{6}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 240 \tan^{4}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{2}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 40} + \frac{15 x}{40 \tan^{8}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{6}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 240 \tan^{4}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{2}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 40} - \frac{40 \tan^{7}{\left(\frac{5 x}{8} - \frac{1}{8} \right)}}{40 \tan^{8}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{6}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 240 \tan^{4}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{2}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 40} + \frac{24 \tan^{5}{\left(\frac{5 x}{8} - \frac{1}{8} \right)}}{40 \tan^{8}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{6}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 240 \tan^{4}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{2}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 40} - \frac{24 \tan^{3}{\left(\frac{5 x}{8} - \frac{1}{8} \right)}}{40 \tan^{8}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{6}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 240 \tan^{4}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{2}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 40} + \frac{40 \tan{\left(\frac{5 x}{8} - \frac{1}{8} \right)}}{40 \tan^{8}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{6}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 240 \tan^{4}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 160 \tan^{2}{\left(\frac{5 x}{8} - \frac{1}{8} \right)} + 40}$$
Gráfica
Respuesta
[src]
4 4 3 3 2 2 3 3
3*cos (1) 3*sin (1) cos (1)*sin(1) cos (1/4)*sin(1/4) 3*cos (1)*sin (1) 3*sin (1)*cos(1) 3*sin (1/4)*cos(1/4)
--------- + --------- + -------------- + ------------------ + ----------------- + ---------------- + --------------------
8 8 2 2 4 10 10
$$\frac{3 \sin^{3}{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}}{10} + \frac{3 \cos^{4}{\left(1 \right)}}{8} + \frac{\sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{2} + \frac{3 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{10} + \frac{\sin{\left(\frac{1}{4} \right)} \cos^{3}{\left(\frac{1}{4} \right)}}{2} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{4} + \frac{3 \sin^{4}{\left(1 \right)}}{8}$$
=
=
4 4 3 3 2 2 3 3
3*cos (1) 3*sin (1) cos (1)*sin(1) cos (1/4)*sin(1/4) 3*cos (1)*sin (1) 3*sin (1)*cos(1) 3*sin (1/4)*cos(1/4)
--------- + --------- + -------------- + ------------------ + ----------------- + ---------------- + --------------------
8 8 2 2 4 10 10
$$\frac{3 \sin^{3}{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}}{10} + \frac{3 \cos^{4}{\left(1 \right)}}{8} + \frac{\sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{2} + \frac{3 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{10} + \frac{\sin{\left(\frac{1}{4} \right)} \cos^{3}{\left(\frac{1}{4} \right)}}{2} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{4} + \frac{3 \sin^{4}{\left(1 \right)}}{8}$$
3*cos(1)^4/8 + 3*sin(1)^4/8 + cos(1)^3*sin(1)/2 + cos(1/4)^3*sin(1/4)/2 + 3*cos(1)^2*sin(1)^2/4 + 3*sin(1)^3*cos(1)/10 + 3*sin(1/4)^3*cos(1/4)/10
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.