Sr Examen
Integral de sin(x+8)^4 dx
Solución
Ha introducido
[src]
1 / | | 4 | sin (x + 8) dx | / 0
$$\int\limits_{0}^{1} \sin^{4}{\left(x + 8 \right)}\, dx$$
Integral(sin(x + 8)^4, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 3/ x\ / x\ 7/ x\ 5/ x\ 8/ x\ 2/ x\ 6/ x\ 4/ x\
| 22*tan |4 + -| 6*tan|4 + -| 6*tan |4 + -| 22*tan |4 + -| 3*x*tan |4 + -| 12*x*tan |4 + -| 12*x*tan |4 + -| 18*x*tan |4 + -|
| 4 \ 2/ \ 2/ 3*x \ 2/ \ 2/ \ 2/ \ 2/ \ 2/ \ 2/
| sin (x + 8) dx = C - -------------------------------------------------------------------- - -------------------------------------------------------------------- + -------------------------------------------------------------------- + -------------------------------------------------------------------- + -------------------------------------------------------------------- + -------------------------------------------------------------------- + -------------------------------------------------------------------- + -------------------------------------------------------------------- + --------------------------------------------------------------------
| 8/ x\ 2/ x\ 6/ x\ 4/ x\ 8/ x\ 2/ x\ 6/ x\ 4/ x\ 8/ x\ 2/ x\ 6/ x\ 4/ x\ 8/ x\ 2/ x\ 6/ x\ 4/ x\ 8/ x\ 2/ x\ 6/ x\ 4/ x\ 8/ x\ 2/ x\ 6/ x\ 4/ x\ 8/ x\ 2/ x\ 6/ x\ 4/ x\ 8/ x\ 2/ x\ 6/ x\ 4/ x\ 8/ x\ 2/ x\ 6/ x\ 4/ x\
/ 8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -| 8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -| 8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -| 8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -| 8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -| 8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -| 8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -| 8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -| 8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -|
\ 2/ \ 2/ \ 2/ \ 2/ \ 2/ \ 2/ \ 2/ \ 2/ \ 2/ \ 2/ \ 2/ \ 2/ \ 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 \sin^{4}{\left(x + 8 \right)}\, dx = C + \frac{3 x \tan^{8}{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} + \frac{12 x \tan^{6}{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} + \frac{18 x \tan^{4}{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} + \frac{12 x \tan^{2}{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} + \frac{3 x}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} + \frac{6 \tan^{7}{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} + \frac{22 \tan^{5}{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} - \frac{22 \tan^{3}{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} - \frac{6 \tan{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8}$$
Gráfica
Respuesta
[src]
4 4 3 3 2 2 3 3
3*cos (9) 3*sin (9) 5*sin (9)*cos(9) 3*cos (9)*sin(9) 3*cos (9)*sin (9) 3*cos (8)*sin(8) 5*sin (8)*cos(8)
--------- + --------- - ---------------- - ---------------- + ----------------- + ---------------- + ----------------
8 8 8 8 4 8 8
$$\frac{5 \sin^{3}{\left(8 \right)} \cos{\left(8 \right)}}{8} + \frac{3 \sin{\left(8 \right)} \cos^{3}{\left(8 \right)}}{8} + \frac{3 \sin^{4}{\left(9 \right)}}{8} - \frac{5 \sin^{3}{\left(9 \right)} \cos{\left(9 \right)}}{8} + \frac{3 \sin^{2}{\left(9 \right)} \cos^{2}{\left(9 \right)}}{4} - \frac{3 \sin{\left(9 \right)} \cos^{3}{\left(9 \right)}}{8} + \frac{3 \cos^{4}{\left(9 \right)}}{8}$$
=
=
4 4 3 3 2 2 3 3
3*cos (9) 3*sin (9) 5*sin (9)*cos(9) 3*cos (9)*sin(9) 3*cos (9)*sin (9) 3*cos (8)*sin(8) 5*sin (8)*cos(8)
--------- + --------- - ---------------- - ---------------- + ----------------- + ---------------- + ----------------
8 8 8 8 4 8 8
$$\frac{5 \sin^{3}{\left(8 \right)} \cos{\left(8 \right)}}{8} + \frac{3 \sin{\left(8 \right)} \cos^{3}{\left(8 \right)}}{8} + \frac{3 \sin^{4}{\left(9 \right)}}{8} - \frac{5 \sin^{3}{\left(9 \right)} \cos{\left(9 \right)}}{8} + \frac{3 \sin^{2}{\left(9 \right)} \cos^{2}{\left(9 \right)}}{4} - \frac{3 \sin{\left(9 \right)} \cos^{3}{\left(9 \right)}}{8} + \frac{3 \cos^{4}{\left(9 \right)}}{8}$$
3*cos(9)^4/8 + 3*sin(9)^4/8 - 5*sin(9)^3*cos(9)/8 - 3*cos(9)^3*sin(9)/8 + 3*cos(9)^2*sin(9)^2/4 + 3*cos(8)^3*sin(8)/8 + 5*sin(8)^3*cos(8)/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.