32768*(120*cosh(x)^2+120* ... osh(x)*sinh(x)) если x=-4 (упростите выражение)

Вы ввели

      /        2              2          2    /       2\       2    /       2\                       \
32768*\120*cosh (x) + 120*sinh (x) + cosh (x)*\1 + 2*x / + sinh (x)*\1 + 2*x / + 64*x*cosh(x)*sinh(x)/

$$32768 \left(64 x \cosh{\left (x \right )} \sinh{\left (x \right )} + \left(2 x^{2} + 1\right) \sinh^{2}{\left (x \right )} + \left(2 x^{2} + 1\right) \cosh^{2}{\left (x \right )} + 120 \sinh^{2}{\left (x \right )} + 120 \cosh^{2}{\left (x \right )}\right)$$

Подстановка условия

32768*(120*cosh(x)^2 + 120*sinh(x)^2 + cosh(x)^2*(1 + 2*x^2) + sinh(x)^2*(1 + 2*x^2) + ((64*x)*cosh(x))*sinh(x)) при x = -4

32768*(120*cosh(x)^2 + 120*sinh(x)^2 + cosh(x)^2*(1 + 2*x^2) + sinh(x)^2*(1 + 2*x^2) + ((64*x)*cosh(x))*sinh(x))

$$32768 \left(64 x \cosh{\left (x \right )} \sinh{\left (x \right )} + \left(2 x^{2} + 1\right) \sinh^{2}{\left (x \right )} + \left(2 x^{2} + 1\right) \cosh^{2}{\left (x \right )} + 120 \sinh^{2}{\left (x \right )} + 120 \cosh^{2}{\left (x \right )}\right)$$

32768*(120*cosh((-4))^2 + 120*sinh((-4))^2 + cosh((-4))^2*(1 + 2*(-4)^2) + sinh((-4))^2*(1 + 2*(-4)^2) + ((64*(-4))*cosh((-4)))*sinh((-4)))

$$32768 \left(64 (-4) \cosh{\left ((-4) \right )} \sinh{\left ((-4) \right )} + \left(2 (-4)^{2} + 1\right) \sinh^{2}{\left ((-4) \right )} + \left(2 (-4)^{2} + 1\right) \cosh^{2}{\left ((-4) \right )} + 120 \sinh^{2}{\left ((-4) \right )} + 120 \cosh^{2}{\left ((-4) \right )}\right)$$

32768*(120*cosh(-4)^2 + 120*sinh(-4)^2 + cosh(-4)^2*(1 + 2*(-4)^2) + sinh(-4)^2*(1 + 2*(-4)^2) + ((64*(-4))*cosh(-4))*sinh(-4))

$$32768 \left(-4 \cdot 64 \cosh{\left (-4 \right )} \sinh{\left (-4 \right )} + \left(1 + 2 \left(-4\right)^{2}\right) \sinh^{2}{\left (-4 \right )} + \left(1 + 2 \left(-4\right)^{2}\right) \cosh^{2}{\left (-4 \right )} + 120 \sinh^{2}{\left (-4 \right )} + 120 \cosh^{2}{\left (-4 \right )}\right)$$

5013504*cosh(4)^2 + 5013504*sinh(4)^2 + 8388608*cosh(4)*sinh(4)

$$5013504 \sinh^{2}{\left (4 \right )} + 5013504 \cosh^{2}{\left (4 \right )} + 8388608 \sinh{\left (4 \right )} \cosh{\left (4 \right )}$$

Степени

            2                  2                2    /       2\             2    /       2\                            
3932160*cosh (x) + 3932160*sinh (x) + 32768*cosh (x)*\1 + 2*x / + 32768*sinh (x)*\1 + 2*x / + 2097152*x*cosh(x)*sinh(x)

$$2097152 x \sinh{\left (x \right )} \cosh{\left (x \right )} + 32768 \left(2 x^{2} + 1\right) \sinh^{2}{\left (x \right )} + 32768 \left(2 x^{2} + 1\right) \cosh^{2}{\left (x \right )} + 3932160 \sinh^{2}{\left (x \right )} + 3932160 \cosh^{2}{\left (x \right )}$$

Численный ответ

3932160.0*cosh(x)^2 + 3932160.0*sinh(x)^2 + 32768.0*cosh(x)^2*(1.0 + 2.0*x^2) + 32768.0*sinh(x)^2*(1.0 + 2.0*x^2) + 2097152.0*x*cosh(x)*sinh(x)

Рациональный знаменатель

            2                  2                2    /       2\             2    /       2\                            
3932160*cosh (x) + 3932160*sinh (x) + 32768*cosh (x)*\1 + 2*x / + 32768*sinh (x)*\1 + 2*x / + 2097152*x*cosh(x)*sinh(x)

$$2097152 x \sinh{\left (x \right )} \cosh{\left (x \right )} + 32768 \left(2 x^{2} + 1\right) \sinh^{2}{\left (x \right )} + 32768 \left(2 x^{2} + 1\right) \cosh^{2}{\left (x \right )} + 3932160 \sinh^{2}{\left (x \right )} + 3932160 \cosh^{2}{\left (x \right )}$$

Объединение рациональных выражений

            2                  2                2    /       2\             2    /       2\                            
3932160*cosh (x) + 3932160*sinh (x) + 32768*cosh (x)*\1 + 2*x / + 32768*sinh (x)*\1 + 2*x / + 2097152*x*cosh(x)*sinh(x)

$$2097152 x \sinh{\left (x \right )} \cosh{\left (x \right )} + 32768 \left(2 x^{2} + 1\right) \sinh^{2}{\left (x \right )} + 32768 \left(2 x^{2} + 1\right) \cosh^{2}{\left (x \right )} + 3932160 \sinh^{2}{\left (x \right )} + 3932160 \cosh^{2}{\left (x \right )}$$

Общее упрощение

                           2                                
3964928*cosh(2*x) + 65536*x *cosh(2*x) + 1048576*x*sinh(2*x)

$$65536 x^{2} \cosh{\left (2 x \right )} + 1048576 x \sinh{\left (2 x \right )} + 3964928 \cosh{\left (2 x \right )}$$

Собрать выражение

            2                  2                2    /       2\             2    /       2\                             
3932160*cosh (x) + 3932160*sinh (x) + 32768*cosh (x)*\1 + 2*x / + 32768*sinh (x)*\1 + 2*x / + 32768*64*x*cosh(x)*sinh(x)

$$32768 \cdot 64 x \cosh{\left (x \right )} \sinh{\left (x \right )} + 32768 \left(2 x^{2} + 1\right) \sinh^{2}{\left (x \right )} + 32768 \left(2 x^{2} + 1\right) \cosh^{2}{\left (x \right )} + 3932160 \sinh^{2}{\left (x \right )} + 3932160 \cosh^{2}{\left (x \right )}$$

Общий знаменатель

            2                  2             2     2             2     2                               
3964928*cosh (x) + 3964928*sinh (x) + 65536*x *cosh (x) + 65536*x *sinh (x) + 2097152*x*cosh(x)*sinh(x)

$$65536 x^{2} \sinh^{2}{\left (x \right )} + 65536 x^{2} \cosh^{2}{\left (x \right )} + 2097152 x \sinh{\left (x \right )} \cosh{\left (x \right )} + 3964928 \sinh^{2}{\left (x \right )} + 3964928 \cosh^{2}{\left (x \right )}$$

Тригонометрическая часть

                           2                                
3964928*cosh(2*x) + 65536*x *cosh(2*x) + 1048576*x*sinh(2*x)

$$65536 x^{2} \cosh{\left (2 x \right )} + 1048576 x \sinh{\left (2 x \right )} + 3964928 \cosh{\left (2 x \right )}$$

Комбинаторика

      /        2              2         2     2         2     2                          \
32768*\121*cosh (x) + 121*sinh (x) + 2*x *cosh (x) + 2*x *sinh (x) + 64*x*cosh(x)*sinh(x)/

$$32768 \left(2 x^{2} \sinh^{2}{\left (x \right )} + 2 x^{2} \cosh^{2}{\left (x \right )} + 64 x \sinh{\left (x \right )} \cosh{\left (x \right )} + 121 \sinh^{2}{\left (x \right )} + 121 \cosh^{2}{\left (x \right )}\right)$$