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