integral of ((sin(2x))/y+x)

Lösung

\int (\frac{sin ( 2 x )}{y} + x) d x

- \frac{1}{2 y} cos (2 x) + \frac{x ^{2}}{2} + C

Schritte zur Lösung

\int \frac{sin ( 2 x )}{y} + x d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{sin ( 2 x )}{y} d x + \int x d x

\int \frac{sin ( 2 x )}{y} d x = - \frac{1}{2 y} cos (2 x)

\int x d x = \frac{x ^{2}}{2}

= - \frac{1}{2 y} cos (2 x) + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2 y} cos (2 x) + \frac{x ^{2}}{2} + C

\int \frac{2 x}{x ^{2} - 2 x + 2} d x

\int \frac{3}{x ^{4}} - \frac{2}{x} d x

\int 8 cot^{4} (t) d t

\int \frac{1}{2 x ^{2} + 8 x + 10} d x

\int \frac{2 x ^{2} + 1}{( x - 2 ) ^{3}} d x