integral of y^3+10xy^4-2x

Lösung

\int y^{3} + 10 x y^{4} - 2 x d x

y^{3} x - x^{2} + 5 y^{4} x^{2} + C

Schritte zur Lösung

\int y^{3} + 10 x y^{4} - 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 y^{3} d x - \int 2 x d x + \int 10 y^{4} x d x

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

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

\int 10 y^{4} x d x = 5 y^{4} x^{2}

= y^{3} x - x^{2} + 5 y^{4} x^{2}

Füge eine Konstante zur Lösung hinzu

= y^{3} x - x^{2} + 5 y^{4} x^{2} + C

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

d er i v a t i v e f (x) = x 8 - x^{2}

\frac{d}{d x} (\frac{x + 2}{x + 3})

\int \frac{sin ( x )}{7 - cos ^{2} ( x )} d x

d er i v a t i v e \frac{x ^{2}}{x ^{2} - 1}