integral of 4x^3-xy+cos(y)

Lösung

\int 4 x^{3} - x y + cos (y) d x

cos (y) x + x^{4} - \frac{y x ^{2}}{2} + C

Schritte zur Lösung

\int 4 x^{3} - x y + cos (y) 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 cos (y) d x + \int 4 x^{3} d x - \int y x d x

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

\int 4 x^{3} d x = x^{4}

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

= cos (y) x + x^{4} - \frac{y x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= cos (y) x + x^{4} - \frac{y x ^{2}}{2} + C

\int \frac{r}{r ^{2} + 1} d r

\int \frac{1}{y ( 1 + y )} d y

\int sin (\frac{1}{5} x) sin (\frac{1}{10} x) d x

\int 2 e^{2 x} x d x

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