de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of sqrt(x)(x^2+3x-8)

Lösung

\int x (x^{2} + 3 x - 8) d x

Lösung

\frac{2}{7} x^{\frac{7}{2}} + \frac{6}{5} x^{\frac{5}{2}} - \frac{16}{3} x^{\frac{3}{2}} + C

Schritte zur Lösung

\int x (x^{2} + 3 x - 8) d x

Multipliziere aus

x (x^{2} + 3 x - 8) : x^{\frac{5}{2}} + 3 x^{\frac{3}{2}} - 8 x

= \int x^{\frac{5}{2}} + 3 x^{\frac{3}{2}} - 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 x^{\frac{5}{2}} d x + \int 3 x^{\frac{3}{2}} d x - \int 8 x d x

\int x^{\frac{5}{2}} d x = \frac{2}{7} x^{\frac{7}{2}}

\int 3 x^{\frac{3}{2}} d x = \frac{6}{5} x^{\frac{5}{2}}

\int 8 x d x = \frac{16}{3} x^{\frac{3}{2}}

= \frac{2}{7} x^{\frac{7}{2}} + \frac{6}{5} x^{\frac{5}{2}} - \frac{16}{3} x^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{7} x^{\frac{7}{2}} + \frac{6}{5} x^{\frac{5}{2}} - \frac{16}{3} x^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

integral of 1/(x^8+x)

\int \frac{1}{x ^{8} + x} d x

integral of (2/(sqrt(1-x^2)))

\int (\frac{2}{1 - x ^{2}}) d x

integral of (20(1-x^2))/(x^2+1)

\int \frac{20 ( 1 - x ^{2} )}{x ^{2} + 1} d x

integral of (e^{sin(x)})

\int (e^{s i n (x)}) d x

integral of (ln(1+sqrt(x)))/(1+sqrt(x))

\int \frac{ln ( 1 + x )}{1 + x} d x