integral (300)/((2x+1))+12x^3-8x

Lösung

integral

\frac{300}{( 2 x + 1 )} + 12 x^{3} - 8 x

150 ln ∣ 2 x + 1 ∣ + 3 x^{4} - 4 x^{2} + C

Schritte zur Lösung

\int \frac{300}{2 x + 1} + 12 x^{3} - 8 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 \frac{300}{2 x + 1} d x + \int 12 x^{3} d x - \int 8 x d x

\int \frac{300}{2 x + 1} d x = 150 ln ∣ 2 x + 1 ∣

\int 12 x^{3} d x = 3 x^{4}

\int 8 x d x = 4 x^{2}

= 150 ln ∣ 2 x + 1 ∣ + 3 x^{4} - 4 x^{2}

Füge eine Konstante zur Lösung hinzu

= 150 ln ∣ 2 x + 1 ∣ + 3 x^{4} - 4 x^{2} + C

in t e g r a l sin^{5} (\frac{x}{3}) cos (\frac{x}{3})

in t e g r a l \frac{1}{1} + x^{2} \frac{x ^{2}}{2}

in t e g r a l \frac{1}{x} (arctan (\frac{1}{x}))

in t e g r a l - 4 e^{3} x

in t e g r a l tan (\frac{x}{2})