Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan(7*x)^2*(21+21*tan(7*x)^2)/log(3*x+2)-3*tan(7*x)^3/((3*x+2)*log(3*x+2)^2)
¿Cómo vas a descomponer esta tan(7*x)^2*(21+21*tan(7*x)^2)/log(3*x+2)-3*tan(7*x)^3/((3*x+2)*log(3*x+2)^2) expresión en fracciones?
Solución
Ha introducido
[src]
2 / 2 \ 3
tan (7*x)*\21 + 21*tan (7*x)/ 3*tan (7*x)
----------------------------- - -----------------------
log(3*x + 2) 2
(3*x + 2)*log (3*x + 2)
$$\frac{\left(21 \tan^{2}{\left(7 x \right)} + 21\right) \tan^{2}{\left(7 x \right)}}{\log{\left(3 x + 2 \right)}} - \frac{3 \tan^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2}}$$
(tan(7*x)^2*(21 + 21*tan(7*x)^2))/log(3*x + 2) - 3*tan(7*x)^3/((3*x + 2)*log(3*x + 2)^2)
Simplificación general
[src]
2 / 7*(2 + 3*x)*log(2 + 3*x)\
3*tan (7*x)*|-tan(7*x) + ------------------------|
| 2 |
\ cos (7*x) /
--------------------------------------------------
2
(2 + 3*x)*log (2 + 3*x)
$$\frac{3 \left(\frac{7 \left(3 x + 2\right) \log{\left(3 x + 2 \right)}}{\cos^{2}{\left(7 x \right)}} - \tan{\left(7 x \right)}\right) \tan^{2}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2}}$$
3*tan(7*x)^2*(-tan(7*x) + 7*(2 + 3*x)*log(2 + 3*x)/cos(7*x)^2)/((2 + 3*x)*log(2 + 3*x)^2)
Respuesta numérica
[src]
tan(7*x)^2*(21.0 + 21.0*tan(7*x)^2)/log(3*x + 2) - 3.0*tan(7*x)^3/((2.0 + 3.0*x)*log(3*x + 2)^2)
tan(7*x)^2*(21.0 + 21.0*tan(7*x)^2)/log(3*x + 2) - 3.0*tan(7*x)^3/((2.0 + 3.0*x)*log(3*x + 2)^2)
Unión de expresiones racionales
[src]
2 / / 2 \ \
3*tan (7*x)*\-tan(7*x) + 7*\1 + tan (7*x)/*(2 + 3*x)*log(2 + 3*x)/
------------------------------------------------------------------
2
(2 + 3*x)*log (2 + 3*x)
$$\frac{3 \left(7 \left(3 x + 2\right) \left(\tan^{2}{\left(7 x \right)} + 1\right) \log{\left(3 x + 2 \right)} - \tan{\left(7 x \right)}\right) \tan^{2}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2}}$$
3*tan(7*x)^2*(-tan(7*x) + 7*(1 + tan(7*x)^2)*(2 + 3*x)*log(2 + 3*x))/((2 + 3*x)*log(2 + 3*x)^2)
Denominador racional
[src]
3 2 2 2 4 2 2 2 4
- 3*tan (7*x)*log(2 + 3*x) + 42*log (2 + 3*x)*tan (7*x) + 42*log (2 + 3*x)*tan (7*x) + 63*x*log (2 + 3*x)*tan (7*x) + 63*x*log (2 + 3*x)*tan (7*x)
--------------------------------------------------------------------------------------------------------------------------------------------------
3
(2 + 3*x)*log (2 + 3*x)
$$\frac{63 x \log{\left(3 x + 2 \right)}^{2} \tan^{4}{\left(7 x \right)} + 63 x \log{\left(3 x + 2 \right)}^{2} \tan^{2}{\left(7 x \right)} + 42 \log{\left(3 x + 2 \right)}^{2} \tan^{4}{\left(7 x \right)} + 42 \log{\left(3 x + 2 \right)}^{2} \tan^{2}{\left(7 x \right)} - 3 \log{\left(3 x + 2 \right)} \tan^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{3}}$$
(-3*tan(7*x)^3*log(2 + 3*x) + 42*log(2 + 3*x)^2*tan(7*x)^2 + 42*log(2 + 3*x)^2*tan(7*x)^4 + 63*x*log(2 + 3*x)^2*tan(7*x)^2 + 63*x*log(2 + 3*x)^2*tan(7*x)^4)/((2 + 3*x)*log(2 + 3*x)^3)
Combinatoria
[src]
2 / 2 2 \
3*tan (7*x)*\-tan(7*x) + 14*log(2 + 3*x) + 14*tan (7*x)*log(2 + 3*x) + 21*x*log(2 + 3*x) + 21*x*tan (7*x)*log(2 + 3*x)/
-----------------------------------------------------------------------------------------------------------------------
2
(2 + 3*x)*log (2 + 3*x)
$$\frac{3 \left(21 x \log{\left(3 x + 2 \right)} \tan^{2}{\left(7 x \right)} + 21 x \log{\left(3 x + 2 \right)} + 14 \log{\left(3 x + 2 \right)} \tan^{2}{\left(7 x \right)} + 14 \log{\left(3 x + 2 \right)} - \tan{\left(7 x \right)}\right) \tan^{2}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2}}$$
3*tan(7*x)^2*(-tan(7*x) + 14*log(2 + 3*x) + 14*tan(7*x)^2*log(2 + 3*x) + 21*x*log(2 + 3*x) + 21*x*tan(7*x)^2*log(2 + 3*x))/((2 + 3*x)*log(2 + 3*x)^2)
Denominador común
[src]
3 2 4 2 4
- 3*tan (7*x) + 42*tan (7*x)*log(2 + 3*x) + 42*tan (7*x)*log(2 + 3*x) + 63*x*tan (7*x)*log(2 + 3*x) + 63*x*tan (7*x)*log(2 + 3*x)
---------------------------------------------------------------------------------------------------------------------------------
2 2
2*log (2 + 3*x) + 3*x*log (2 + 3*x)
$$\frac{63 x \log{\left(3 x + 2 \right)} \tan^{4}{\left(7 x \right)} + 63 x \log{\left(3 x + 2 \right)} \tan^{2}{\left(7 x \right)} + 42 \log{\left(3 x + 2 \right)} \tan^{4}{\left(7 x \right)} + 42 \log{\left(3 x + 2 \right)} \tan^{2}{\left(7 x \right)} - 3 \tan^{3}{\left(7 x \right)}}{3 x \log{\left(3 x + 2 \right)}^{2} + 2 \log{\left(3 x + 2 \right)}^{2}}$$
(-3*tan(7*x)^3 + 42*tan(7*x)^2*log(2 + 3*x) + 42*tan(7*x)^4*log(2 + 3*x) + 63*x*tan(7*x)^2*log(2 + 3*x) + 63*x*tan(7*x)^4*log(2 + 3*x))/(2*log(2 + 3*x)^2 + 3*x*log(2 + 3*x)^2)
Parte trigonométrica
[src]
2
/ 2/7*x\\ 2/7*x\
3 84*|1 + tan |---|| *tan |---|
3*tan (7*x) \ \ 2 // \ 2 /
- ----------------------- + -----------------------------
2 4
(2 + 3*x)*log (2 + 3*x) / 2/7*x\\
|1 - tan |---|| *log(2 + 3*x)
\ \ 2 //
$$- \frac{3 \tan^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2}} + \frac{84 \left(\tan^{2}{\left(\frac{7 x}{2} \right)} + 1\right)^{2} \tan^{2}{\left(\frac{7 x}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{7 x}{2} \right)}\right)^{4} \log{\left(3 x + 2 \right)}}$$
3 2
3*tan (7*x) 21*tan (7*x)
- ----------------------- + ----------------------------------------
2 2
(2 + 3*x)*log (2 + 3*x) / 2/7*x\\ 4/7*x\
|-1 + cot |---|| *log(2 + 3*x)*sin |---|
\ \ 2 // \ 2 /
$$\frac{21 \tan^{2}{\left(7 x \right)}}{\left(\cot^{2}{\left(\frac{7 x}{2} \right)} - 1\right)^{2} \log{\left(3 x + 2 \right)} \sin^{4}{\left(\frac{7 x}{2} \right)}} - \frac{3 \tan^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2}}$$
/ 2/ pi\\
| 21*cos |7*x - --||
2/ pi\ | \ 2 /|
cos |7*x - --|*|21 + -----------------| 3/ pi\
\ 2 / | 2 | 3*cos |7*x - --|
\ cos (7*x) / \ 2 /
--------------------------------------- - ---------------------------------
2 3 2
cos (7*x)*log(2 + 3*x) (2 + 3*x)*cos (7*x)*log (2 + 3*x)
$$\frac{\left(21 + \frac{21 \cos^{2}{\left(7 x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(7 x \right)}}\right) \cos^{2}{\left(7 x - \frac{\pi}{2} \right)}}{\log{\left(3 x + 2 \right)} \cos^{2}{\left(7 x \right)}} - \frac{3 \cos^{3}{\left(7 x - \frac{\pi}{2} \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2} \cos^{3}{\left(7 x \right)}}$$
2/7*x\
3 84*tan |---|
3*tan (7*x) \ 2 /
- ----------------------- + ---------------------------------------
2 4
(2 + 3*x)*log (2 + 3*x) / 2/7*x\\ 4/7*x\
|1 - tan |---|| *cos |---|*log(2 + 3*x)
\ \ 2 // \ 2 /
$$- \frac{3 \tan^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2}} + \frac{84 \tan^{2}{\left(\frac{7 x}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{7 x}{2} \right)}\right)^{4} \log{\left(3 x + 2 \right)} \cos^{4}{\left(\frac{7 x}{2} \right)}}$$
/ 2 \
2 | 21*sin (7*x)|
sin (7*x)*|21 + ------------|
| 2 | 3
\ cos (7*x) / 3*sin (7*x)
----------------------------- - ---------------------------------
2 3 2
cos (7*x)*log(2 + 3*x) (2 + 3*x)*cos (7*x)*log (2 + 3*x)
$$\frac{\left(\frac{21 \sin^{2}{\left(7 x \right)}}{\cos^{2}{\left(7 x \right)}} + 21\right) \sin^{2}{\left(7 x \right)}}{\log{\left(3 x + 2 \right)} \cos^{2}{\left(7 x \right)}} - \frac{3 \sin^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2} \cos^{3}{\left(7 x \right)}}$$
3 4 2
3*tan (7*x) 21*sec (7*x)*sin (7*x)
- ----------------------- + ----------------------
2 log(2 + 3*x)
(2 + 3*x)*log (2 + 3*x)
$$\frac{21 \sin^{2}{\left(7 x \right)} \sec^{4}{\left(7 x \right)}}{\log{\left(3 x + 2 \right)}} - \frac{3 \tan^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2}}$$
3 2
3*tan (7*x) 21*sin (7*x)
- ----------------------- + ----------------------
2 4
(2 + 3*x)*log (2 + 3*x) cos (7*x)*log(2 + 3*x)
$$\frac{21 \sin^{2}{\left(7 x \right)}}{\log{\left(3 x + 2 \right)} \cos^{4}{\left(7 x \right)}} - \frac{3 \tan^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2}}$$
2
/ 2/7*x\\ 2
3 21*|1 + tan |---|| *tan (7*x)
3*tan (7*x) \ \ 2 //
- ----------------------- + -----------------------------
2 2
(2 + 3*x)*log (2 + 3*x) / 2/7*x\\
|1 - tan |---|| *log(2 + 3*x)
\ \ 2 //
$$- \frac{3 \tan^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2}} + \frac{21 \left(\tan^{2}{\left(\frac{7 x}{2} \right)} + 1\right)^{2} \tan^{2}{\left(7 x \right)}}{\left(1 - \tan^{2}{\left(\frac{7 x}{2} \right)}\right)^{2} \log{\left(3 x + 2 \right)}}$$
21
21 + ---------
2
cot (7*x) 3
---------------------- - ---------------------------------
2 3 2
cot (7*x)*log(2 + 3*x) (2 + 3*x)*cot (7*x)*log (2 + 3*x)
$$\frac{21 + \frac{21}{\cot^{2}{\left(7 x \right)}}}{\log{\left(3 x + 2 \right)} \cot^{2}{\left(7 x \right)}} - \frac{3}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2} \cot^{3}{\left(7 x \right)}}$$
2/ pi\ 3/ pi\
21*cos |7*x - --| 3*cos |7*x - --|
\ 2 / \ 2 /
---------------------- - ---------------------------------
4 3 2
cos (7*x)*log(2 + 3*x) (2 + 3*x)*cos (7*x)*log (2 + 3*x)
$$\frac{21 \cos^{2}{\left(7 x - \frac{\pi}{2} \right)}}{\log{\left(3 x + 2 \right)} \cos^{4}{\left(7 x \right)}} - \frac{3 \cos^{3}{\left(7 x - \frac{\pi}{2} \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2} \cos^{3}{\left(7 x \right)}}$$
6 4
24*sin (7*x) 84*sin (7*x)
- ---------------------------------- + --------------------------------------
2 3 2 2/pi \
(2 + 3*x)*log (2 + 3*x)*sin (14*x) log(2 + 3*x)*sin (14*x)*sin |-- + 7*x|
\2 /
$$\frac{84 \sin^{4}{\left(7 x \right)}}{\log{\left(3 x + 2 \right)} \sin^{2}{\left(14 x \right)} \sin^{2}{\left(7 x + \frac{\pi}{2} \right)}} - \frac{24 \sin^{6}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2} \sin^{3}{\left(14 x \right)}}$$
3 2
3*tan (7*x) 21*tan (7*x)
- ----------------------- + ---------------------------------------
2 2
(2 + 3*x)*log (2 + 3*x) / 2/7*x\\ 4/7*x\
|1 - tan |---|| *cos |---|*log(2 + 3*x)
\ \ 2 // \ 2 /
$$- \frac{3 \tan^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2}} + \frac{21 \tan^{2}{\left(7 x \right)}}{\left(1 - \tan^{2}{\left(\frac{7 x}{2} \right)}\right)^{2} \log{\left(3 x + 2 \right)} \cos^{4}{\left(\frac{7 x}{2} \right)}}$$
2/7*x\
3 84*cot |---|
3*tan (7*x) \ 2 /
- ----------------------- + ----------------------------------------
2 4
(2 + 3*x)*log (2 + 3*x) / 2/7*x\\ 4/7*x\
|-1 + cot |---|| *log(2 + 3*x)*sin |---|
\ \ 2 // \ 2 /
$$\frac{84 \cot^{2}{\left(\frac{7 x}{2} \right)}}{\left(\cot^{2}{\left(\frac{7 x}{2} \right)} - 1\right)^{4} \log{\left(3 x + 2 \right)} \sin^{4}{\left(\frac{7 x}{2} \right)}} - \frac{3 \tan^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2}}$$
2
/ 2/7*x\\
21*|1 + cot |---||
3 \ \ 2 //
- --------------------------------- + ----------------------------------------
3 2 2
(2 + 3*x)*cot (7*x)*log (2 + 3*x) / 2/7*x\\ 2
|-1 + cot |---|| *cot (7*x)*log(2 + 3*x)
\ \ 2 //
$$\frac{21 \left(\cot^{2}{\left(\frac{7 x}{2} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{7 x}{2} \right)} - 1\right)^{2} \log{\left(3 x + 2 \right)} \cot^{2}{\left(7 x \right)}} - \frac{3}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2} \cot^{3}{\left(7 x \right)}}$$
/ 2/pi \\
| 21*csc |-- - 7*x||
2/pi \ | \2 /|
csc |-- - 7*x|*|21 + -----------------| 3/pi \
\2 / | 2 | 3*csc |-- - 7*x|
\ csc (7*x) / \2 /
--------------------------------------- - ---------------------------------
2 3 2
csc (7*x)*log(2 + 3*x) (2 + 3*x)*csc (7*x)*log (2 + 3*x)
$$\frac{\left(21 + \frac{21 \csc^{2}{\left(- 7 x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(7 x \right)}}\right) \csc^{2}{\left(- 7 x + \frac{\pi}{2} \right)}}{\log{\left(3 x + 2 \right)} \csc^{2}{\left(7 x \right)}} - \frac{3 \csc^{3}{\left(- 7 x + \frac{\pi}{2} \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2} \csc^{3}{\left(7 x \right)}}$$
3 2
3*tan (7*x) 21*tan (7*x)
- ----------------------- + ----------------------
2 2
(2 + 3*x)*log (2 + 3*x) cos (7*x)*log(2 + 3*x)
$$\frac{21 \tan^{2}{\left(7 x \right)}}{\log{\left(3 x + 2 \right)} \cos^{2}{\left(7 x \right)}} - \frac{3 \tan^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2}}$$
4 3
21*sec (7*x) 3*sec (7*x)
--------------------------- - --------------------------------------
2/ pi\ 2 3/ pi\
log(2 + 3*x)*sec |7*x - --| (2 + 3*x)*log (2 + 3*x)*sec |7*x - --|
\ 2 / \ 2 /
$$\frac{21 \sec^{4}{\left(7 x \right)}}{\log{\left(3 x + 2 \right)} \sec^{2}{\left(7 x - \frac{\pi}{2} \right)}} - \frac{3 \sec^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2} \sec^{3}{\left(7 x - \frac{\pi}{2} \right)}}$$
/ 2 \
2 | 21*sec (7*x)|
sec (7*x)*|21 + ------------|
| 2 | 3
\ csc (7*x) / 3*sec (7*x)
----------------------------- - ---------------------------------
2 3 2
csc (7*x)*log(2 + 3*x) (2 + 3*x)*csc (7*x)*log (2 + 3*x)
$$\frac{\left(21 + \frac{21 \sec^{2}{\left(7 x \right)}}{\csc^{2}{\left(7 x \right)}}\right) \sec^{2}{\left(7 x \right)}}{\log{\left(3 x + 2 \right)} \csc^{2}{\left(7 x \right)}} - \frac{3 \sec^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2} \csc^{3}{\left(7 x \right)}}$$
/ 4 \
4 | 84*sin (7*x)|
4*sin (7*x)*|21 + ------------|
6 | 2 |
24*sin (7*x) \ sin (14*x) /
- ---------------------------------- + -------------------------------
2 3 2
(2 + 3*x)*log (2 + 3*x)*sin (14*x) log(2 + 3*x)*sin (14*x)
$$\frac{4 \left(\frac{84 \sin^{4}{\left(7 x \right)}}{\sin^{2}{\left(14 x \right)}} + 21\right) \sin^{4}{\left(7 x \right)}}{\log{\left(3 x + 2 \right)} \sin^{2}{\left(14 x \right)}} - \frac{24 \sin^{6}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2} \sin^{3}{\left(14 x \right)}}$$
4/pi \ 3/pi \
21*csc |-- - 7*x| 3*csc |-- - 7*x|
\2 / \2 /
---------------------- - ---------------------------------
2 3 2
csc (7*x)*log(2 + 3*x) (2 + 3*x)*csc (7*x)*log (2 + 3*x)
$$\frac{21 \csc^{4}{\left(- 7 x + \frac{\pi}{2} \right)}}{\log{\left(3 x + 2 \right)} \csc^{2}{\left(7 x \right)}} - \frac{3 \csc^{3}{\left(- 7 x + \frac{\pi}{2} \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2} \csc^{3}{\left(7 x \right)}}$$
2 6
21*sin (7*x) 24*sin (7*x)
--------------------------- - ----------------------------------
4/pi \ 2 3
log(2 + 3*x)*sin |-- + 7*x| (2 + 3*x)*log (2 + 3*x)*sin (14*x)
\2 /
$$\frac{21 \sin^{2}{\left(7 x \right)}}{\log{\left(3 x + 2 \right)} \sin^{4}{\left(7 x + \frac{\pi}{2} \right)}} - \frac{24 \sin^{6}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2} \sin^{3}{\left(14 x \right)}}$$
3 2
3*tan (7*x) 21*tan (7*x)
- ----------------------- + ----------------------
2 2
(3*x + 2)*log (3*x + 2) cos (7*x)*log(3*x + 2)
$$\frac{21 \tan^{2}{\left(7 x \right)}}{\log{\left(3 x + 2 \right)} \cos^{2}{\left(7 x \right)}} - \frac{3 \tan^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2}}$$
2
/ 2/7*x\\ 2/7*x\
84*|1 + cot |---|| *cot |---|
3 \ \ 2 // \ 2 /
- --------------------------------- + ------------------------------
3 2 4
(2 + 3*x)*cot (7*x)*log (2 + 3*x) / 2/7*x\\
|-1 + cot |---|| *log(2 + 3*x)
\ \ 2 //
$$\frac{84 \left(\cot^{2}{\left(\frac{7 x}{2} \right)} + 1\right)^{2} \cot^{2}{\left(\frac{7 x}{2} \right)}}{\left(\cot^{2}{\left(\frac{7 x}{2} \right)} - 1\right)^{4} \log{\left(3 x + 2 \right)}} - \frac{3}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2} \cot^{3}{\left(7 x \right)}}$$
/ 2 \
2 | 21*sec (7*x) |
sec (7*x)*|21 + --------------|
| 2/ pi\|
| sec |7*x - --|| 3
\ \ 2 // 3*sec (7*x)
------------------------------- - --------------------------------------
2/ pi\ 2 3/ pi\
log(2 + 3*x)*sec |7*x - --| (2 + 3*x)*log (2 + 3*x)*sec |7*x - --|
\ 2 / \ 2 /
$$\frac{\left(\frac{21 \sec^{2}{\left(7 x \right)}}{\sec^{2}{\left(7 x - \frac{\pi}{2} \right)}} + 21\right) \sec^{2}{\left(7 x \right)}}{\log{\left(3 x + 2 \right)} \sec^{2}{\left(7 x - \frac{\pi}{2} \right)}} - \frac{3 \sec^{3}{\left(7 x \right)}}{\left(3 x + 2\right) \log{\left(3 x + 2 \right)}^{2} \sec^{3}{\left(7 x - \frac{\pi}{2} \right)}}$$
sec(7*x)^2*(21 + 21*sec(7*x)^2/sec(7*x - pi/2)^2)/(log(2 + 3*x)*sec(7*x - pi/2)^2) - 3*sec(7*x)^3/((2 + 3*x)*log(2 + 3*x)^2*sec(7*x - pi/2)^3)
Potencias
[src]
/ 2\
2 | / 7*I*x -7*I*x\ |
/ 7*I*x -7*I*x\ | 21*\- e + e / |
\- e + e / *|21 - ------------------------|
| 2 | 3
| / -7*I*x 7*I*x\ | / 7*I*x -7*I*x\
\ \e + e / / 3*I*\- e + e /
- ----------------------------------------------------- + -------------------------------------------
2 3
/ -7*I*x 7*I*x\ / -7*I*x 7*I*x\ 2
\e + e / *log(2 + 3*x) (2 + 3*x)*\e + e / *log (2 + 3*x)
$$- \frac{\left(- \frac{21 \left(- e^{7 i x} + e^{- 7 i x}\right)^{2}}{\left(e^{7 i x} + e^{- 7 i x}\right)^{2}} + 21\right) \left(- e^{7 i x} + e^{- 7 i x}\right)^{2}}{\left(e^{7 i x} + e^{- 7 i x}\right)^{2} \log{\left(3 x + 2 \right)}} + \frac{3 i \left(- e^{7 i x} + e^{- 7 i x}\right)^{3}}{\left(3 x + 2\right) \left(e^{7 i x} + e^{- 7 i x}\right)^{3} \log{\left(3 x + 2 \right)}^{2}}$$
-(-exp(7*i*x) + exp(-7*i*x))^2*(21 - 21*(-exp(7*i*x) + exp(-7*i*x))^2/(exp(-7*i*x) + exp(7*i*x))^2)/((exp(-7*i*x) + exp(7*i*x))^2*log(2 + 3*x)) + 3*i*(-exp(7*i*x) + exp(-7*i*x))^3/((2 + 3*x)*(exp(-7*i*x) + exp(7*i*x))^3*log(2 + 3*x)^2)