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Beliebt Rechnen >

integral of (y^2+16)/y

Lösung

\int \frac{y ^{2} + 16}{y} d y

Lösung

\frac{y ^{2}}{2} + 16 ln ∣ y ∣ + C

Schritte zur Lösung

\int \frac{y ^{2} + 16}{y} d y

Multipliziere aus

\frac{y ^{2} + 16}{y} : y + \frac{16}{y}

= \int y + \frac{16}{y} d y

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 d y + \int \frac{16}{y} d y

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

\int \frac{16}{y} d y = 16 ln ∣ y ∣

= \frac{y ^{2}}{2} + 16 ln ∣ y ∣

Füge eine Konstante zur Lösung hinzu

= \frac{y ^{2}}{2} + 16 ln ∣ y ∣ + C

Graph

Beliebte Beispiele

derivative of ln((x^3-2x/(4+x)))

\frac{d}{d x} (ln (\frac{x ^{3} - 2 x}{4 + x}))

derivative f(x)=(2x+1)/(x+2)

d er i v a t i v e f (x) = \frac{2 x + 1}{x + 2}

derivative of (sqrt(x)/2)

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

11x-6ysqrt(x^2+1)(dy)/(dx)=0,y(0)=9

11 x - 6 y x^{2} + 1 \frac{d y}{d x} = 0, y (0) = 9

derivative y=(2/((2x-6) 3/2))

d er i v a t i v e y = (\frac{2}{( 2 x - 6 ) \frac{3}{2}})