integral of x-1+4sin(2x)

Lösung

\int x - 1 + 4 sin (2 x) d x

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

Schritte zur Lösung

\int x - 1 + 4 sin (2 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 x d x - \int 1 d x + \int 4 sin (2 x) d x

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

\int 1 d x = x

\int 4 sin (2 x) d x = - 2 cos (2 x)

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{x}{3 x - 12} d x

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

\int \frac{x}{1 - x x} d x

\int (7 x^{3} + 2 3 x^{2}) d x

\int (\frac{sin ( ln ( x ) )}{x}) d x