de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (2x+1)sqrt(4x-3)

Lösung

\int (2 x + 1) 4 x - 3 d x

Lösung

\frac{1}{5} x (4 x - 3)^{\frac{3}{2}} + \frac{4}{15} (4 x - 3)^{\frac{3}{2}} + C

Schritte zur Lösung

\int (2 x + 1) 4 x - 3 d x

Multipliziere aus

(2 x + 1) 4 x - 3 : 2 x 4 x - 3 + 4 x - 3

= \int 2 x 4 x - 3 + 4 x - 3 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 2 x 4 x - 3 d x + \int 4 x - 3 d x

\int 2 x 4 x - 3 d x = \frac{1}{10} (2 x + 1) (4 x - 3)^{\frac{3}{2}}

\int 4 x - 3 d x = \frac{1}{6} (4 x - 3)^{\frac{3}{2}}

= \frac{1}{10} (2 x + 1) (4 x - 3)^{\frac{3}{2}} + \frac{1}{6} (4 x - 3)^{\frac{3}{2}}

Vereinfache

\frac{1}{10} (2 x + 1) (4 x - 3)^{\frac{3}{2}} + \frac{1}{6} (4 x - 3)^{\frac{3}{2}} : \frac{1}{5} x (4 x - 3)^{\frac{3}{2}} + \frac{4}{15} (4 x - 3)^{\frac{3}{2}}

= \frac{1}{5} x (4 x - 3)^{\frac{3}{2}} + \frac{4}{15} (4 x - 3)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} x (4 x - 3)^{\frac{3}{2}} + \frac{4}{15} (4 x - 3)^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

integral of (e^xx)/((x+1)^2)

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

integral of x(9x^2+7)^3

\int x (9 x^{2} + 7)^{3} d x

integral of (2x^2+7x+6)/(x^3+2x^2+2x)

\int \frac{2 x ^{2} + 7 x + 6}{x ^{3} + 2 x ^{2} + 2 x} d x

integral of sin^3(X)

\int sin^{3} (X) d X

integral of (5t^2+7)/(t^{3/4)}

\int \frac{5 t ^{2} + 7}{t ^{\frac{3}{4}}} d t