Sr Examen
Integral de cos^3(1-x) dx
Solución
Ha introducido
[src]
1 / | | 3 | cos (1 - x) dx | / 0
$$\int\limits_{0}^{1} \cos^{3}{\left(1 - x \right)}\, dx$$
Integral(cos(1 - x)^3, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 3/ 1 x\ 5/ 1 x\ / 1 x\
| 4*tan |- - + -| 6*tan |- - + -| 6*tan|- - + -|
| 3 \ 2 2/ \ 2 2/ \ 2 2/
| cos (1 - x) dx = C + ------------------------------------------------------- + ------------------------------------------------------- + -------------------------------------------------------
| 6/ 1 x\ 2/ 1 x\ 4/ 1 x\ 6/ 1 x\ 2/ 1 x\ 4/ 1 x\ 6/ 1 x\ 2/ 1 x\ 4/ 1 x\
/ 3 + 3*tan |- - + -| + 9*tan |- - + -| + 9*tan |- - + -| 3 + 3*tan |- - + -| + 9*tan |- - + -| + 9*tan |- - + -| 3 + 3*tan |- - + -| + 9*tan |- - + -| + 9*tan |- - + -|
\ 2 2/ \ 2 2/ \ 2 2/ \ 2 2/ \ 2 2/ \ 2 2/ \ 2 2/ \ 2 2/ \ 2 2/
$$\int \cos^{3}{\left(1 - x \right)}\, dx = C + \frac{6 \tan^{5}{\left(\frac{x}{2} - \frac{1}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} - \frac{1}{2} \right)} + 9 \tan^{4}{\left(\frac{x}{2} - \frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} - \frac{1}{2} \right)} + 3} + \frac{4 \tan^{3}{\left(\frac{x}{2} - \frac{1}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} - \frac{1}{2} \right)} + 9 \tan^{4}{\left(\frac{x}{2} - \frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} - \frac{1}{2} \right)} + 3} + \frac{6 \tan{\left(\frac{x}{2} - \frac{1}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} - \frac{1}{2} \right)} + 9 \tan^{4}{\left(\frac{x}{2} - \frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} - \frac{1}{2} \right)} + 3}$$
Gráfica
Respuesta
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3
2*sin (1) 2
--------- + cos (1)*sin(1)
3
$$\sin{\left(1 \right)} \cos^{2}{\left(1 \right)} + \frac{2 \sin^{3}{\left(1 \right)}}{3}$$
=
=
3
2*sin (1) 2
--------- + cos (1)*sin(1)
3
$$\sin{\left(1 \right)} \cos^{2}{\left(1 \right)} + \frac{2 \sin^{3}{\left(1 \right)}}{3}$$
2*sin(1)^3/3 + cos(1)^2*sin(1)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.