integral of 3x^2+y^2

Lösung

\int 3 x^{2} + y^{2} d x

y^{2} x + x^{3} + C

Schritte zur Lösung

\int 3 x^{2} + y^{2} 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^{2} d x + \int 3 x^{2} d x

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

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

= y^{2} x + x^{3}

Füge eine Konstante zur Lösung hinzu

= y^{2} x + x^{3} + C

x \to 6 lim (\frac{1}{x})

\frac{d x}{d t} = x^{\frac{1}{2}}

s im pl i f y f (5)

a re a 5 cos (x), 5 cos (2 x), [0, π]

\int \frac{cos ^{5} ( 3 x )}{sin ^{14} ( 3 x )} d x