integral from 1 to 4 of (x^2+4)/x

Lösung

\int_{1}^{4} \frac{x ^{2} + 4}{x} d x

\frac{15}{2} + 8 ln (2)

Dezimale

13.04517 \dots

Schritte zur Lösung

\int_{1}^{4} \frac{x ^{2} + 4}{x} d x

Multipliziere aus

\frac{x ^{2} + 4}{x} : x + \frac{4}{x}

= \int_{1}^{4} x + \frac{4}{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_{1}^{4} x d x + \int_{1}^{4} \frac{4}{x} d x

\int_{1}^{4} x d x = \frac{15}{2}

\int_{1}^{4} \frac{4}{x} d x = 8 ln (2)

= \frac{15}{2} + 8 ln (2)

\frac{d}{d x} (\frac{x ^{2} + 6}{( 2 x - 7 ) ^{7}})

x \to 0 lim (\frac{200 π}{x})

n or ma l y = \frac{y + 5 x}{3 y - x}, (1, 2)

\frac{d}{d x} (e^{2 t a n (x)})

d er i v a t i v e 1 + t