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

Soluzione

espandere

\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}

Fasi della soluzione

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

Espandi

\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}

Unisci

\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}

Applica la regola delle frazioni:

\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}

Applica la regola delle frazioni:

\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}

Cancellare

\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}

Dividi i numeri:

\frac{4}{4} = 1

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

s im pl i f y 3 (2 - 2)

s im pl i f y (\frac{2}{7} - \frac{1}{x}) \cdot (\frac{5}{x} + \frac{1}{3})

s im pl i f y 4 ((\frac{19}{12})^{\frac{1}{24}} - 1)

s im pl i f y (x - 3) (x - 5)

e x p an d (vx + x x^{2} - v^{2}) d x - x (H (x) d x + x d v = 0)