What is expand (3/4 (2tsin(2t)+cos(2t))+C)/t ?

The solution to expand (3/4 (2tsin(2t)+cos(2t))+C)/t is (3sin(2t))/2+(3cos(2t))/(4t)+C/t

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expand (3/4 (2tsin(2t)+cos(2t))+C)/t

expand

\frac{\frac{3}{4} ( 2 t sin ( 2 t ) + cos ( 2 t ) ) + C}{t}

\frac{3 sin ( 2 t )}{2} + \frac{3 cos ( 2 t )}{4 t} + \frac{C}{t}

Solution steps

\frac{\frac{3}{4} ( 2 t sin ( 2 t ) + cos ( 2 t ) ) + C}{t}

Expand

\frac{3}{4} (2 t sin (2 t) + cos (2 t)) + C : \frac{3 t sin ( 2 t )}{2} + \frac{3}{4} cos (2 t) + C

= \frac{\frac{3 t s i n ( 2 t )}{2} + \frac{3}{4} cos ( 2 t ) + C}{t}

Join

\frac{3 t sin ( 2 t )}{2} + \frac{3}{4} cos (2 t) + C : \frac{6 t sin ( 2 t ) + 3 cos ( 2 t ) + 4 C}{4}

= \frac{\frac{6 t s i n ( 2 t ) + 3 c o s ( 2 t ) + 4 C}{4}}{t}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{6 t sin ( 2 t ) + 3 cos ( 2 t ) + C \cdot 4}{4 t}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{6 t sin ( 2 t ) + 3 cos ( 2 t ) + C \cdot 4}{4 t} = \frac{6 t sin ( 2 t )}{4 t} + \frac{3 cos ( 2 t )}{4 t} + \frac{C \cdot 4}{4 t}

= \frac{6 t sin ( 2 t )}{4 t} + \frac{3 cos ( 2 t )}{4 t} + \frac{4 C}{4 t}

Cancel

\frac{6 t sin ( 2 t )}{4 t} : \frac{3 sin ( 2 t )}{2}

= \frac{3 sin ( 2 t )}{2} + \frac{3 cos ( 2 t )}{4 t} + \frac{4 C}{4 t}

Divide the numbers:

\frac{4}{4} = 1

= \frac{3 sin ( 2 t )}{2} + \frac{3 cos ( 2 t )}{4 t} + \frac{C}{t}

3 (2 - 2)

(\frac{2}{7} - \frac{1}{x}) \cdot (\frac{5}{x} + \frac{1}{3})

4 ((\frac{19}{12})^{\frac{1}{24}} - 1)

\frac{\partial}{\partial z} ((x) (0.5 x - 0.5 y - z))

(x - 3) (x - 5)

What is expand (3/4 (2tsin(2t)+cos(2t))+C)/t ?
The solution to expand (3/4 (2tsin(2t)+cos(2t))+C)/t is (3sin(2t))/2+(3cos(2t))/(4t)+C/t