integral of (sin(x)+cos(x)-x)

Lösung

\int (sin (x) + cos (x) - x) d x

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

Schritte zur Lösung

\int sin (x) + cos (x) - 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 sin (x) d x + \int cos (x) d x - \int x d x

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

\int cos (x) d x = sin (x)

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

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{1}{( 2 x - 1 ) 4 ( 2 x - 1 ) ^{2} - 2} d x

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

\int t e^{t} d t

\int \frac{ln ( 3 x )}{x} d x

\int \frac{16 x ^{3}}{25 - 16 x ^{8}} d x