Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sin(sqrt(x))^(1/(x^2))*(-2*log(sin(sqrt(x)))/x^3+cos(sqrt(x))/(2*x^(5/2)*sin(sqrt(x))))
¿Cómo vas a descomponer esta sin(sqrt(x))^(1/(x^2))*(-2*log(sin(sqrt(x)))/x^3+cos(sqrt(x))/(2*x^(5/2)*sin(sqrt(x)))) expresión en fracciones?
Solución
Ha introducido
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1
--
2
x / / / ___\\ / ___\ \
/ / ___\\ |-2*log\sin\\/ x // cos\\/ x / |
\sin\\/ x // *|------------------ + -----------------|
| 3 5/2 / ___\|
\ x 2*x *sin\\/ x //
$$\left(\frac{\cos{\left(\sqrt{x} \right)}}{2 x^{\frac{5}{2}} \sin{\left(\sqrt{x} \right)}} + \frac{\left(-1\right) 2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{x^{3}}\right) \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)}$$
sin(sqrt(x))^(1/(x^2))*((-2*log(sin(sqrt(x))))/x^3 + cos(sqrt(x))/(((2*x^(5/2))*sin(sqrt(x)))))
Simplificación general
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1
-1 + --
2
x
/ / ___\\ / 3 / ___\ 5/2 / / ___\\ / ___\\
\sin\\/ x // *\x *cos\\/ x / - 4*x *log\sin\\/ x //*sin\\/ x //
-----------------------------------------------------------------------
11/2
2*x
$$\frac{\left(- 4 x^{\frac{5}{2}} \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \sin{\left(\sqrt{x} \right)} + x^{3} \cos{\left(\sqrt{x} \right)}\right) \sin^{-1 + \frac{1}{x^{2}}}{\left(\sqrt{x} \right)}}{2 x^{\frac{11}{2}}}$$
sin(sqrt(x))^(-1 + x^(-2))*(x^3*cos(sqrt(x)) - 4*x^(5/2)*log(sin(sqrt(x)))*sin(sqrt(x)))/(2*x^(11/2))
Respuesta numérica
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sin(sqrt(x))^(x^(-2))*(-2.0*log(sin(sqrt(x)))/x^3 + 0.5*x^(-2.5)*cos(sqrt(x))/sin(sqrt(x)))
sin(sqrt(x))^(x^(-2))*(-2.0*log(sin(sqrt(x)))/x^3 + 0.5*x^(-2.5)*cos(sqrt(x))/sin(sqrt(x)))
Denominador común
[src]
1 1
-- --
2 2
x x
3 / / ___\\ / ___\ 5/2 / / ___\\ / / ___\\ / ___\
x *\sin\\/ x // *cos\\/ x / - 4*x *\sin\\/ x // *log\sin\\/ x //*sin\\/ x /
-------------------------------------------------------------------------------
11/2 / ___\
2*x *sin\\/ x /
$$\frac{- 4 x^{\frac{5}{2}} \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \sin{\left(\sqrt{x} \right)} \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)} + x^{3} \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)} \cos{\left(\sqrt{x} \right)}}{2 x^{\frac{11}{2}} \sin{\left(\sqrt{x} \right)}}$$
(x^3*sin(sqrt(x))^(x^(-2))*cos(sqrt(x)) - 4*x^(5/2)*sin(sqrt(x))^(x^(-2))*log(sin(sqrt(x)))*sin(sqrt(x)))/(2*x^(11/2)*sin(sqrt(x)))
Combinatoria
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1
--
2
x
/ / ___\\ / 3 / ___\ 5/2 / / ___\\ / ___\\
\sin\\/ x // *\x *cos\\/ x / - 4*x *log\sin\\/ x //*sin\\/ x //
------------------------------------------------------------------
11/2 / ___\
2*x *sin\\/ x /
$$\frac{\left(- 4 x^{\frac{5}{2}} \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \sin{\left(\sqrt{x} \right)} + x^{3} \cos{\left(\sqrt{x} \right)}\right) \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)}}{2 x^{\frac{11}{2}} \sin{\left(\sqrt{x} \right)}}$$
sin(sqrt(x))^(x^(-2))*(x^3*cos(sqrt(x)) - 4*x^(5/2)*log(sin(sqrt(x)))*sin(sqrt(x)))/(2*x^(11/2)*sin(sqrt(x)))
Unión de expresiones racionales
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1
--
2
x
/ / ___\\ / 3 / ___\ 5/2 / / ___\\ / ___\\
\sin\\/ x // *\x *cos\\/ x / - 4*x *log\sin\\/ x //*sin\\/ x //
------------------------------------------------------------------
11/2 / ___\
2*x *sin\\/ x /
$$\frac{\left(- 4 x^{\frac{5}{2}} \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \sin{\left(\sqrt{x} \right)} + x^{3} \cos{\left(\sqrt{x} \right)}\right) \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)}}{2 x^{\frac{11}{2}} \sin{\left(\sqrt{x} \right)}}$$
sin(sqrt(x))^(x^(-2))*(x^3*cos(sqrt(x)) - 4*x^(5/2)*log(sin(sqrt(x)))*sin(sqrt(x)))/(2*x^(11/2)*sin(sqrt(x)))
Compilar la expresión
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1
--
2
x / / / ___\\ / ___\ \
/ / ___\\ | 2*log\sin\\/ x // cos\\/ x / |
\sin\\/ x // *|- ----------------- + -----------------|
| 3 5/2 / ___\|
\ x 2*x *sin\\/ x //
$$\left(- \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{x^{3}} + \frac{\cos{\left(\sqrt{x} \right)}}{2 x^{\frac{5}{2}} \sin{\left(\sqrt{x} \right)}}\right) \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)}$$
sin(sqrt(x))^(1/(x^2))*(-2*log(sin(sqrt(x)))/x^3 + cos(sqrt(x))/(2*x^(5/2)*sin(sqrt(x))))
Parte trigonométrica
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/ / / ___\ \ \
1 | | |\/ x | | |
-- | | 2*tan|-----| | |
2 | | \ 2 / | |
x | 2*log|---------------| |
/ / ___\ \ | | / ___\| / ___\ |
| |\/ x | | | | 2|\/ x || 2|\/ x | |
| 2*tan|-----| | | |1 + tan |-----|| 1 - tan |-----| |
| \ 2 / | | \ \ 2 // \ 2 / |
|---------------| *|- ---------------------- + -----------------|
| / ___\| | 3 / ___\|
| 2|\/ x || | x 5/2 |\/ x ||
|1 + tan |-----|| | 4*x *tan|-----||
\ \ 2 // \ \ 2 //
$$\left(\frac{2 \tan{\left(\frac{\sqrt{x}}{2} \right)}}{\tan^{2}{\left(\frac{\sqrt{x}}{2} \right)} + 1}\right)^{\frac{1}{x^{2}}} \left(- \frac{2 \log{\left(\frac{2 \tan{\left(\frac{\sqrt{x}}{2} \right)}}{\tan^{2}{\left(\frac{\sqrt{x}}{2} \right)} + 1} \right)}}{x^{3}} + \frac{1 - \tan^{2}{\left(\frac{\sqrt{x}}{2} \right)}}{4 x^{\frac{5}{2}} \tan{\left(\frac{\sqrt{x}}{2} \right)}}\right)$$
1
-- / / ___\ / ___\\
2 | |\/ x | |\/ x ||
x | / / ___\\ - tan|-----| + cot|-----||
/ / ___\\ | 2*log\sin\\/ x // \ 2 / \ 2 /|
\sin\\/ x // *|- ----------------- + -------------------------|
| 3 5/2 |
\ x 4*x /
$$\left(- \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{x^{3}} + \frac{- \tan{\left(\frac{\sqrt{x}}{2} \right)} + \cot{\left(\frac{\sqrt{x}}{2} \right)}}{4 x^{\frac{5}{2}}}\right) \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)}$$
/ / ___\\
| 1 |\/ x ||
1 | ---------- - tan|-----||
-- | / ___\ \ 2 /|
2 | |\/ x | |
x | / / ___\\ tan|-----| |
/ / ___\\ | 2*log\sin\\/ x // \ 2 / |
\sin\\/ x // *|- ----------------- + -----------------------|
| 3 5/2 |
\ x 4*x /
$$\left(- \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{x^{3}} + \frac{- \tan{\left(\frac{\sqrt{x}}{2} \right)} + \frac{1}{\tan{\left(\frac{\sqrt{x}}{2} \right)}}}{4 x^{\frac{5}{2}}}\right) \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)}$$
1
--
2 / / ___ pi\ \
x | / / ___\\ sin|\/ x + --| |
/ / ___\\ | 2*log\sin\\/ x // \ 2 / |
\sin\\/ x // *|- ----------------- + -----------------|
| 3 5/2 / ___\|
\ x 2*x *sin\\/ x //
$$\left(- \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{x^{3}} + \frac{\sin{\left(\sqrt{x} + \frac{\pi}{2} \right)}}{2 x^{\frac{5}{2}} \sin{\left(\sqrt{x} \right)}}\right) \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)}$$
/ / ___\\
| 2|\/ x ||
| / ___\ 2*sin |-----||
| sin\\/ x / \ 2 /|
1 | ------------- - -------------|
-- | / ___\ / ___\ |
2 | 2|\/ x | sin\\/ x / |
x | / / ___\\ 2*sin |-----| |
/ / ___\\ | 2*log\sin\\/ x // \ 2 / |
\sin\\/ x // *|- ----------------- + -----------------------------|
| 3 5/2 |
\ x 4*x /
$$\left(- \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{x^{3}} + \frac{- \frac{2 \sin^{2}{\left(\frac{\sqrt{x}}{2} \right)}}{\sin{\left(\sqrt{x} \right)}} + \frac{\sin{\left(\sqrt{x} \right)}}{2 \sin^{2}{\left(\frac{\sqrt{x}}{2} \right)}}}{4 x^{\frac{5}{2}}}\right) \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)}$$
1
-- / / 1 \ \
2 | 2*log|----------| |
x | | / ___\| / ___\ |
/ 1 \ | \csc\\/ x // csc\\/ x / |
|----------| *|- ----------------- + ----------------------|
| / ___\| | 3 5/2 /pi ___\|
\csc\\/ x // | x 2*x *csc|-- - \/ x ||
\ \2 //
$$\left(- \frac{2 \log{\left(\frac{1}{\csc{\left(\sqrt{x} \right)}} \right)}}{x^{3}} + \frac{\csc{\left(\sqrt{x} \right)}}{2 x^{\frac{5}{2}} \csc{\left(- \sqrt{x} + \frac{\pi}{2} \right)}}\right) \left(\frac{1}{\csc{\left(\sqrt{x} \right)}}\right)^{\frac{1}{x^{2}}}$$
1
--
2
x / / ___\ / / ___\\\
/ / ___\\ |cot\\/ x / 2*log\sin\\/ x //|
\sin\\/ x // *|---------- - -----------------|
| 5/2 3 |
\ 2*x x /
$$\left(- \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{x^{3}} + \frac{\cot{\left(\sqrt{x} \right)}}{2 x^{\frac{5}{2}}}\right) \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)}$$
/ / / ___\ \ \
1 | | |\/ x | | |
-- | | 2*cot|-----| | |
2 | | \ 2 / | |
x | 2*log|---------------| |
/ / ___\ \ | | / ___\| / ___\|
| |\/ x | | | | 2|\/ x || 2|\/ x ||
| 2*cot|-----| | | |1 + cot |-----|| -1 + cot |-----||
| \ 2 / | | \ \ 2 // \ 2 /|
|---------------| *|- ---------------------- + -----------------|
| / ___\| | 3 / ___\|
| 2|\/ x || | x 5/2 |\/ x ||
|1 + cot |-----|| | 4*x *cot|-----||
\ \ 2 // \ \ 2 //
$$\left(\frac{2 \cot{\left(\frac{\sqrt{x}}{2} \right)}}{\cot^{2}{\left(\frac{\sqrt{x}}{2} \right)} + 1}\right)^{\frac{1}{x^{2}}} \left(- \frac{2 \log{\left(\frac{2 \cot{\left(\frac{\sqrt{x}}{2} \right)}}{\cot^{2}{\left(\frac{\sqrt{x}}{2} \right)} + 1} \right)}}{x^{3}} + \frac{\cot^{2}{\left(\frac{\sqrt{x}}{2} \right)} - 1}{4 x^{\frac{5}{2}} \cot{\left(\frac{\sqrt{x}}{2} \right)}}\right)$$
/ / ___\ / ___\\
| |\/ x | |pi \/ x ||
| csc|-----| csc|-- - -----||
| \ 2 / \2 2 /|
1 | --------------- - ---------------|
-- | / 1 \ / ___\ / ___\ |
2 | 2*log|----------| |pi \/ x | |\/ x | |
x | | / ___\| csc|-- - -----| csc|-----| |
/ 1 \ | \csc\\/ x // \2 2 / \ 2 / |
|----------| *|- ----------------- + ---------------------------------|
| / ___\| | 3 5/2 |
\csc\\/ x // \ x 4*x /
$$\left(- \frac{2 \log{\left(\frac{1}{\csc{\left(\sqrt{x} \right)}} \right)}}{x^{3}} + \frac{\frac{\csc{\left(\frac{\sqrt{x}}{2} \right)}}{\csc{\left(- \frac{\sqrt{x}}{2} + \frac{\pi}{2} \right)}} - \frac{\csc{\left(- \frac{\sqrt{x}}{2} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{\sqrt{x}}{2} \right)}}}{4 x^{\frac{5}{2}}}\right) \left(\frac{1}{\csc{\left(\sqrt{x} \right)}}\right)^{\frac{1}{x^{2}}}$$
1
-- / / 1 \ \
2 | 2*log|----------| |
x | | / ___\| / ___\ |
/ 1 \ | \csc\\/ x // csc\\/ x / |
|----------| *|- ----------------- + -----------------|
| / ___\| | 3 5/2 / ___\|
\csc\\/ x // \ x 2*x *sec\\/ x //
$$\left(- \frac{2 \log{\left(\frac{1}{\csc{\left(\sqrt{x} \right)}} \right)}}{x^{3}} + \frac{\csc{\left(\sqrt{x} \right)}}{2 x^{\frac{5}{2}} \sec{\left(\sqrt{x} \right)}}\right) \left(\frac{1}{\csc{\left(\sqrt{x} \right)}}\right)^{\frac{1}{x^{2}}}$$
/ / ___ \ / ___\ \
| |\/ x pi| |\/ x | |
| sec|----- - --| sec|-----| |
| \ 2 2 / \ 2 / |
1 | / 1 \ --------------- - ---------------|
-- | 2*log|---------------| / ___\ / ___ \|
2 | | / ___ pi\| |\/ x | |\/ x pi||
x | |sec|\/ x - --|| sec|-----| sec|----- - --||
/ 1 \ | \ \ 2 // \ 2 / \ 2 2 /|
|---------------| *|- ---------------------- + ---------------------------------|
| / ___ pi\| | 3 5/2 |
|sec|\/ x - --|| \ x 4*x /
\ \ 2 //
$$\left(- \frac{2 \log{\left(\frac{1}{\sec{\left(\sqrt{x} - \frac{\pi}{2} \right)}} \right)}}{x^{3}} + \frac{- \frac{\sec{\left(\frac{\sqrt{x}}{2} \right)}}{\sec{\left(\frac{\sqrt{x}}{2} - \frac{\pi}{2} \right)}} + \frac{\sec{\left(\frac{\sqrt{x}}{2} - \frac{\pi}{2} \right)}}{\sec{\left(\frac{\sqrt{x}}{2} \right)}}}{4 x^{\frac{5}{2}}}\right) \left(\frac{1}{\sec{\left(\sqrt{x} - \frac{\pi}{2} \right)}}\right)^{\frac{1}{x^{2}}}$$
1
--
2 / / / ___ pi\\ \
x | 2*log|cos|\/ x - --|| / ___\ |
/ / ___ pi\\ | \ \ 2 // cos\\/ x / |
|cos|\/ x - --|| *|- ---------------------- + ----------------------|
\ \ 2 // | 3 5/2 / ___ pi\|
| x 2*x *cos|\/ x - --||
\ \ 2 //
$$\left(- \frac{2 \log{\left(\cos{\left(\sqrt{x} - \frac{\pi}{2} \right)} \right)}}{x^{3}} + \frac{\cos{\left(\sqrt{x} \right)}}{2 x^{\frac{5}{2}} \cos{\left(\sqrt{x} - \frac{\pi}{2} \right)}}\right) \cos^{\frac{1}{x^{2}}}{\left(\sqrt{x} - \frac{\pi}{2} \right)}$$
/ / / ___\ \\
1 | | |\/ x | ||
-- | | 2*cot|-----| ||
2 | | \ 2 / ||
x | 2*log|---------------||
/ / ___\ \ | | / ___\||
| |\/ x | | | | 2|\/ x |||
| 2*cot|-----| | | / ___\ |1 + cot |-----|||
| \ 2 / | |cot\\/ x / \ \ 2 //|
|---------------| *|---------- - ----------------------|
| / ___\| | 5/2 3 |
| 2|\/ x || \ 2*x x /
|1 + cot |-----||
\ \ 2 //
$$\left(\frac{2 \cot{\left(\frac{\sqrt{x}}{2} \right)}}{\cot^{2}{\left(\frac{\sqrt{x}}{2} \right)} + 1}\right)^{\frac{1}{x^{2}}} \left(- \frac{2 \log{\left(\frac{2 \cot{\left(\frac{\sqrt{x}}{2} \right)}}{\cot^{2}{\left(\frac{\sqrt{x}}{2} \right)} + 1} \right)}}{x^{3}} + \frac{\cot{\left(\sqrt{x} \right)}}{2 x^{\frac{5}{2}}}\right)$$
/ / ___\ / ___ \\
| |\/ x | |\/ x pi||
| cos|-----| cos|----- - --||
| \ 2 / \ 2 2 /|
1 | --------------- - ---------------|
-- | / ___ \ / ___\ |
2 | / / ___ pi\\ |\/ x pi| |\/ x | |
x | 2*log|cos|\/ x - --|| cos|----- - --| cos|-----| |
/ / ___ pi\\ | \ \ 2 // \ 2 2 / \ 2 / |
|cos|\/ x - --|| *|- ---------------------- + ---------------------------------|
\ \ 2 // | 3 5/2 |
\ x 4*x /
$$\left(- \frac{2 \log{\left(\cos{\left(\sqrt{x} - \frac{\pi}{2} \right)} \right)}}{x^{3}} + \frac{\frac{\cos{\left(\frac{\sqrt{x}}{2} \right)}}{\cos{\left(\frac{\sqrt{x}}{2} - \frac{\pi}{2} \right)}} - \frac{\cos{\left(\frac{\sqrt{x}}{2} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{\sqrt{x}}{2} \right)}}}{4 x^{\frac{5}{2}}}\right) \cos^{\frac{1}{x^{2}}}{\left(\sqrt{x} - \frac{\pi}{2} \right)}$$
/ / ___\\
| 2|\/ x ||
1 | / ___\ 2*sin |-----||
-- | sin\\/ x / \ 2 /|
2 | -------------- - -------------|
x | / / ___\\ / ___\ / ___\ |
/ / ___\\ | 2*log\sin\\/ x // 1 - cos\\/ x / sin\\/ x / |
\sin\\/ x // *|- ----------------- + ------------------------------|
| 3 5/2 |
\ x 4*x /
$$\left(- \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{x^{3}} + \frac{- \frac{2 \sin^{2}{\left(\frac{\sqrt{x}}{2} \right)}}{\sin{\left(\sqrt{x} \right)}} + \frac{\sin{\left(\sqrt{x} \right)}}{1 - \cos{\left(\sqrt{x} \right)}}}{4 x^{\frac{5}{2}}}\right) \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)}$$
/ / / ___\ \ \
1 | | |\/ x | | |
-- | | 2*tan|-----| | / ___\|
2 | | \ 2 / | 1 |\/ x ||
x | 2*log|---------------| ---------- - tan|-----||
/ / ___\ \ | | / ___\| / ___\ \ 2 /|
| |\/ x | | | | 2|\/ x || |\/ x | |
| 2*tan|-----| | | |1 + tan |-----|| tan|-----| |
| \ 2 / | | \ \ 2 // \ 2 / |
|---------------| *|- ---------------------- + -----------------------|
| / ___\| | 3 5/2 |
| 2|\/ x || \ x 4*x /
|1 + tan |-----||
\ \ 2 //
$$\left(\frac{2 \tan{\left(\frac{\sqrt{x}}{2} \right)}}{\tan^{2}{\left(\frac{\sqrt{x}}{2} \right)} + 1}\right)^{\frac{1}{x^{2}}} \left(- \frac{2 \log{\left(\frac{2 \tan{\left(\frac{\sqrt{x}}{2} \right)}}{\tan^{2}{\left(\frac{\sqrt{x}}{2} \right)} + 1} \right)}}{x^{3}} + \frac{- \tan{\left(\frac{\sqrt{x}}{2} \right)} + \frac{1}{\tan{\left(\frac{\sqrt{x}}{2} \right)}}}{4 x^{\frac{5}{2}}}\right)$$
/ / / ___\ \ \
1 | | |\/ x | | |
-- | | 2*cot|-----| | / ___\|
2 | | \ 2 / | 1 |\/ x ||
x | 2*log|---------------| - ---------- + cot|-----||
/ / ___\ \ | | / ___\| / ___\ \ 2 /|
| |\/ x | | | | 2|\/ x || |\/ x | |
| 2*cot|-----| | | |1 + cot |-----|| cot|-----| |
| \ 2 / | | \ \ 2 // \ 2 / |
|---------------| *|- ---------------------- + -------------------------|
| / ___\| | 3 5/2 |
| 2|\/ x || \ x 4*x /
|1 + cot |-----||
\ \ 2 //
$$\left(\frac{2 \cot{\left(\frac{\sqrt{x}}{2} \right)}}{\cot^{2}{\left(\frac{\sqrt{x}}{2} \right)} + 1}\right)^{\frac{1}{x^{2}}} \left(- \frac{2 \log{\left(\frac{2 \cot{\left(\frac{\sqrt{x}}{2} \right)}}{\cot^{2}{\left(\frac{\sqrt{x}}{2} \right)} + 1} \right)}}{x^{3}} + \frac{\cot{\left(\frac{\sqrt{x}}{2} \right)} - \frac{1}{\cot{\left(\frac{\sqrt{x}}{2} \right)}}}{4 x^{\frac{5}{2}}}\right)$$
1 / / 1 \ \
-- | 2*log|---------------| |
2 | | / ___ pi\| / ___ pi\ |
x | |sec|\/ x - --|| sec|\/ x - --| |
/ 1 \ | \ \ 2 // \ 2 / |
|---------------| *|- ---------------------- + -----------------|
| / ___ pi\| | 3 5/2 / ___\|
|sec|\/ x - --|| \ x 2*x *sec\\/ x //
\ \ 2 //
$$\left(- \frac{2 \log{\left(\frac{1}{\sec{\left(\sqrt{x} - \frac{\pi}{2} \right)}} \right)}}{x^{3}} + \frac{\sec{\left(\sqrt{x} - \frac{\pi}{2} \right)}}{2 x^{\frac{5}{2}} \sec{\left(\sqrt{x} \right)}}\right) \left(\frac{1}{\sec{\left(\sqrt{x} - \frac{\pi}{2} \right)}}\right)^{\frac{1}{x^{2}}}$$
1
--
2
x / / / ___\\ / ___\ \
/ / ___\\ | 2*log\sin\\/ x // cos\\/ x / |
\sin\\/ x // *|- ----------------- + -----------------|
| 3 5/2 / ___\|
\ x 2*x *sin\\/ x //
$$\left(- \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{x^{3}} + \frac{\cos{\left(\sqrt{x} \right)}}{2 x^{\frac{5}{2}} \sin{\left(\sqrt{x} \right)}}\right) \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)}$$
1
--
2
x / / / ___\\\
/ / ___\\ | 1 2*log\sin\\/ x //|
\sin\\/ x // *|----------------- - -----------------|
| 5/2 / ___\ 3 |
\2*x *tan\\/ x / x /
$$\left(- \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{x^{3}} + \frac{1}{2 x^{\frac{5}{2}} \tan{\left(\sqrt{x} \right)}}\right) \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)}$$
/ / / ___\ \\
1 | | |\/ x | ||
-- | | 2*tan|-----| ||
2 | | \ 2 / ||
x | 2*log|---------------||
/ / ___\ \ | | / ___\||
| |\/ x | | | | 2|\/ x |||
| 2*tan|-----| | | |1 + tan |-----|||
| \ 2 / | | 1 \ \ 2 //|
|---------------| *|----------------- - ----------------------|
| / ___\| | 5/2 / ___\ 3 |
| 2|\/ x || \2*x *tan\\/ x / x /
|1 + tan |-----||
\ \ 2 //
$$\left(\frac{2 \tan{\left(\frac{\sqrt{x}}{2} \right)}}{\tan^{2}{\left(\frac{\sqrt{x}}{2} \right)} + 1}\right)^{\frac{1}{x^{2}}} \left(- \frac{2 \log{\left(\frac{2 \tan{\left(\frac{\sqrt{x}}{2} \right)}}{\tan^{2}{\left(\frac{\sqrt{x}}{2} \right)} + 1} \right)}}{x^{3}} + \frac{1}{2 x^{\frac{5}{2}} \tan{\left(\sqrt{x} \right)}}\right)$$
1
--
2
x / / / ___\\ / ___\ \
/ / ___\\ | 2*log\sin\\/ x // sin\2*\/ x / |
\sin\\/ x // *|- ----------------- + ------------------|
| 3 5/2 2/ ___\|
\ x 4*x *sin \\/ x //
$$\left(- \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{x^{3}} + \frac{\sin{\left(2 \sqrt{x} \right)}}{4 x^{\frac{5}{2}} \sin^{2}{\left(\sqrt{x} \right)}}\right) \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)}$$
sin(sqrt(x))^(x^(-2))*(-2*log(sin(sqrt(x)))/x^3 + sin(2*sqrt(x))/(4*x^(5/2)*sin(sqrt(x))^2))
Denominador racional
[src]
1 1
-1 + -- -1 + --
2 2
_____ x _____ x
3 / 11 / / ___\\ / ___\ 5/2 / 11 / / ___\\ / / ___\\ / ___\
x *\/ x *\sin\\/ x // *cos\\/ x / - 4*x *\/ x *\sin\\/ x // *log\sin\\/ x //*sin\\/ x /
-----------------------------------------------------------------------------------------------------------
11
2*x
$$\frac{- 4 x^{\frac{5}{2}} \sqrt{x^{11}} \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \sin{\left(\sqrt{x} \right)} \sin^{-1 + \frac{1}{x^{2}}}{\left(\sqrt{x} \right)} + x^{3} \sqrt{x^{11}} \sin^{-1 + \frac{1}{x^{2}}}{\left(\sqrt{x} \right)} \cos{\left(\sqrt{x} \right)}}{2 x^{11}}$$
(x^3*sqrt(x^11)*sin(sqrt(x))^(-1 + x^(-2))*cos(sqrt(x)) - 4*x^(5/2)*sqrt(x^11)*sin(sqrt(x))^(-1 + x^(-2))*log(sin(sqrt(x)))*sin(sqrt(x)))/(2*x^11)
Potencias
[src]
1
--
2 / / / ___ ___\ \ / ___ ___\ \
x | | | -I*\/ x I*\/ x | | | I*\/ x -I*\/ x | |
/ / ___ ___\ \ | |-I*\- e + e / | |e e | |
| | -I*\/ x I*\/ x | | | 2*log|----------------------------| I*|-------- + ---------| |
|-I*\- e + e / | | \ 2 / \ 2 2 / |
|----------------------------| *|- ----------------------------------- + -----------------------------|
\ 2 / | 3 / ___ ___\|
| x 5/2 | -I*\/ x I*\/ x ||
\ x *\- e + e //
$$\left(- \frac{i \left(e^{i \sqrt{x}} - e^{- i \sqrt{x}}\right)}{2}\right)^{\frac{1}{x^{2}}} \left(- \frac{2 \log{\left(- \frac{i \left(e^{i \sqrt{x}} - e^{- i \sqrt{x}}\right)}{2} \right)}}{x^{3}} + \frac{i \left(\frac{e^{i \sqrt{x}}}{2} + \frac{e^{- i \sqrt{x}}}{2}\right)}{x^{\frac{5}{2}} \left(e^{i \sqrt{x}} - e^{- i \sqrt{x}}\right)}\right)$$
1
--
2
x / / / ___\\ / ___\ \
/ / ___\\ | 2*log\sin\\/ x // cos\\/ x / |
\sin\\/ x // *|- ----------------- + -----------------|
| 3 5/2 / ___\|
\ x 2*x *sin\\/ x //
$$\left(- \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{x^{3}} + \frac{\cos{\left(\sqrt{x} \right)}}{2 x^{\frac{5}{2}} \sin{\left(\sqrt{x} \right)}}\right) \sin^{\frac{1}{x^{2}}}{\left(\sqrt{x} \right)}$$
sin(sqrt(x))^(x^(-2))*(-2*log(sin(sqrt(x)))/x^3 + cos(sqrt(x))/(2*x^(5/2)*sin(sqrt(x))))