integral of (xy^2+x^2+y+4)

Lösung

\int (x y^{2} + x^{2} + y + 4) d x

4 x + y x + \frac{x ^{3}}{3} + \frac{y ^{2} x ^{2}}{2} + C

Schritte zur Lösung

\int x y^{2} + x^{2} + y + 4 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 4 d x + \int y d x + \int x^{2} d x + \int y^{2} x d x

\int 4 d x = 4 x

\int y d x = y x

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

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

= 4 x + y x + \frac{x ^{3}}{3} + \frac{y ^{2} x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= 4 x + y x + \frac{x ^{3}}{3} + \frac{y ^{2} x ^{2}}{2} + C

d er i v a t i v e f (v) = (v^{- 3} + 3 v^{- 2})^{3}

f (x) = x 5 - x

x \to 4 + lim (x^{3} - c x)

\int e^{- 0.02 x} (e^{- 0.13 x} + 4) d x

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