Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan(5*x+7)^3*(20+20*tan(5*x+7)^2)/(2*x^2+9)-4*x*tan(5*x+7)^4/(2*x^2+9)^2
¿Cómo vas a descomponer esta tan(5*x+7)^3*(20+20*tan(5*x+7)^2)/(2*x^2+9)-4*x*tan(5*x+7)^4/(2*x^2+9)^2 expresión en fracciones?
Solución
Ha introducido
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3 / 2 \ 4
tan (5*x + 7)*\20 + 20*tan (5*x + 7)/ 4*x*tan (5*x + 7)
------------------------------------- - -----------------
2 2
2*x + 9 / 2 \
\2*x + 9/
$$- \frac{4 x \tan^{4}{\left(5 x + 7 \right)}}{\left(2 x^{2} + 9\right)^{2}} + \frac{\left(20 \tan^{2}{\left(5 x + 7 \right)} + 20\right) \tan^{3}{\left(5 x + 7 \right)}}{2 x^{2} + 9}$$
(tan(5*x + 7)^3*(20 + 20*tan(5*x + 7)^2))/(2*x^2 + 9) - (4*x)*tan(5*x + 7)^4/(2*x^2 + 9)^2
Simplificación general
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3 // 2 \ / 2\ \
4*tan (7 + 5*x)*\\1 + tan (7 + 5*x)/*\45 + 10*x / - x*tan(7 + 5*x)/
-------------------------------------------------------------------
2
/ 2\
\9 + 2*x /
$$\frac{4 \left(- x \tan{\left(5 x + 7 \right)} + \left(10 x^{2} + 45\right) \left(\tan^{2}{\left(5 x + 7 \right)} + 1\right)\right) \tan^{3}{\left(5 x + 7 \right)}}{\left(2 x^{2} + 9\right)^{2}}$$
4*tan(7 + 5*x)^3*((1 + tan(7 + 5*x)^2)*(45 + 10*x^2) - x*tan(7 + 5*x))/(9 + 2*x^2)^2
Combinatoria
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3 / 2 2 2 2 \
4*tan (7 + 5*x)*\45 + 10*x + 45*tan (7 + 5*x) - x*tan(7 + 5*x) + 10*x *tan (7 + 5*x)/
--------------------------------------------------------------------------------------
2
/ 2\
\9 + 2*x /
$$\frac{4 \left(10 x^{2} \tan^{2}{\left(5 x + 7 \right)} + 10 x^{2} - x \tan{\left(5 x + 7 \right)} + 45 \tan^{2}{\left(5 x + 7 \right)} + 45\right) \tan^{3}{\left(5 x + 7 \right)}}{\left(2 x^{2} + 9\right)^{2}}$$
4*tan(7 + 5*x)^3*(45 + 10*x^2 + 45*tan(7 + 5*x)^2 - x*tan(7 + 5*x) + 10*x^2*tan(7 + 5*x)^2)/(9 + 2*x^2)^2
Unión de expresiones racionales
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3 / / 2 \ / 2\\
4*tan (7 + 5*x)*\-x*tan(7 + 5*x) + 5*\1 + tan (7 + 5*x)/*\9 + 2*x //
--------------------------------------------------------------------
2
/ 2\
\9 + 2*x /
$$\frac{4 \left(- x \tan{\left(5 x + 7 \right)} + 5 \left(2 x^{2} + 9\right) \left(\tan^{2}{\left(5 x + 7 \right)} + 1\right)\right) \tan^{3}{\left(5 x + 7 \right)}}{\left(2 x^{2} + 9\right)^{2}}$$
4*tan(7 + 5*x)^3*(-x*tan(7 + 5*x) + 5*(1 + tan(7 + 5*x)^2)*(9 + 2*x^2))/(9 + 2*x^2)^2
Potencias
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/ 2\
3 | / I*(7 + 5*x) I*(-7 - 5*x)\ |
/ I*(7 + 5*x) I*(-7 - 5*x)\ | 20*\- e + e / |
I*\- e + e / *|20 - ------------------------------------|
4 | 2 |
/ I*(7 + 5*x) I*(-7 - 5*x)\ | / I*(-7 - 5*x) I*(7 + 5*x)\ |
4*x*\- e + e / \ \e + e / /
- ------------------------------------------- - -------------------------------------------------------------------------------
2 4 3
/ 2\ / I*(-7 - 5*x) I*(7 + 5*x)\ / 2\ / I*(-7 - 5*x) I*(7 + 5*x)\
\9 + 2*x / *\e + e / \9 + 2*x /*\e + e /
$$- \frac{4 x \left(e^{i \left(- 5 x - 7\right)} - e^{i \left(5 x + 7\right)}\right)^{4}}{\left(2 x^{2} + 9\right)^{2} \left(e^{i \left(- 5 x - 7\right)} + e^{i \left(5 x + 7\right)}\right)^{4}} - \frac{i \left(- \frac{20 \left(e^{i \left(- 5 x - 7\right)} - e^{i \left(5 x + 7\right)}\right)^{2}}{\left(e^{i \left(- 5 x - 7\right)} + e^{i \left(5 x + 7\right)}\right)^{2}} + 20\right) \left(e^{i \left(- 5 x - 7\right)} - e^{i \left(5 x + 7\right)}\right)^{3}}{\left(2 x^{2} + 9\right) \left(e^{i \left(- 5 x - 7\right)} + e^{i \left(5 x + 7\right)}\right)^{3}}$$
-4*x*(-exp(i*(7 + 5*x)) + exp(i*(-7 - 5*x)))^4/((9 + 2*x^2)^2*(exp(i*(-7 - 5*x)) + exp(i*(7 + 5*x)))^4) - i*(-exp(i*(7 + 5*x)) + exp(i*(-7 - 5*x)))^3*(20 - 20*(-exp(i*(7 + 5*x)) + exp(i*(-7 - 5*x)))^2/(exp(i*(-7 - 5*x)) + exp(i*(7 + 5*x)))^2)/((9 + 2*x^2)*(exp(i*(-7 - 5*x)) + exp(i*(7 + 5*x)))^3)
Denominador racional
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2 2
4 3 4 / 2\ 3 / 2\ 5
- 36*x*tan (7 + 5*x) - 8*x *tan (7 + 5*x) + 20*\9 + 2*x / *tan (7 + 5*x) + 20*\9 + 2*x / *tan (7 + 5*x)
-------------------------------------------------------------------------------------------------------
3
/ 2\
\9 + 2*x /
$$\frac{- 8 x^{3} \tan^{4}{\left(5 x + 7 \right)} - 36 x \tan^{4}{\left(5 x + 7 \right)} + 20 \left(2 x^{2} + 9\right)^{2} \tan^{5}{\left(5 x + 7 \right)} + 20 \left(2 x^{2} + 9\right)^{2} \tan^{3}{\left(5 x + 7 \right)}}{\left(2 x^{2} + 9\right)^{3}}$$
(-36*x*tan(7 + 5*x)^4 - 8*x^3*tan(7 + 5*x)^4 + 20*(9 + 2*x^2)^2*tan(7 + 5*x)^3 + 20*(9 + 2*x^2)^2*tan(7 + 5*x)^5)/(9 + 2*x^2)^3
Respuesta numérica
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tan(5*x + 7)^3*(20.0 + 20.0*tan(5*x + 7)^2)/(9.0 + 2.0*x^2) - 0.0493827160493827*x*tan(5*x + 7)^4/(1 + 0.222222222222222*x^2)^2
tan(5*x + 7)^3*(20.0 + 20.0*tan(5*x + 7)^2)/(9.0 + 2.0*x^2) - 0.0493827160493827*x*tan(5*x + 7)^4/(1 + 0.222222222222222*x^2)^2
Denominador común
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3 5 4 2 3 2 5
180*tan (7 + 5*x) + 180*tan (7 + 5*x) - 4*x*tan (7 + 5*x) + 40*x *tan (7 + 5*x) + 40*x *tan (7 + 5*x)
-----------------------------------------------------------------------------------------------------
4 2
81 + 4*x + 36*x
$$\frac{40 x^{2} \tan^{5}{\left(5 x + 7 \right)} + 40 x^{2} \tan^{3}{\left(5 x + 7 \right)} - 4 x \tan^{4}{\left(5 x + 7 \right)} + 180 \tan^{5}{\left(5 x + 7 \right)} + 180 \tan^{3}{\left(5 x + 7 \right)}}{4 x^{4} + 36 x^{2} + 81}$$
(180*tan(7 + 5*x)^3 + 180*tan(7 + 5*x)^5 - 4*x*tan(7 + 5*x)^4 + 40*x^2*tan(7 + 5*x)^3 + 40*x^2*tan(7 + 5*x)^5)/(81 + 4*x^4 + 36*x^2)