integral of (x^2)/2 y+x/2 y^2cos(z)

Lösung

\int \frac{x ^{2}}{2} y + \frac{x}{2} y^{2} cos (z) d z

\frac{x ^{2}}{2} yz + \frac{x y ^{2}}{2} sin (z) + C

Schritte zur Lösung

\int \frac{x ^{2}}{2} y + \frac{x}{2} y^{2} cos (z) d z

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{x ^{2}}{2} y d z + \int cos (z) \frac{x}{2} y^{2} d z

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

\int cos (z) \frac{x}{2} y^{2} d z = \frac{x y ^{2}}{2} sin (z)

= \frac{x ^{2}}{2} yz + \frac{x y ^{2}}{2} sin (z)

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} yz + \frac{x y ^{2}}{2} sin (z) + C

\frac{\partial}{\partial u} (e^{u})

\int_{2}^{3} \frac{x}{x ^{2} + 4 x + 20} d x

\frac{\partial}{\partial x} (\frac{x ^{2}}{x + y})

d er i v a t i v e x \cdot ln (x)

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