de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

3 x^{3} ln (x + 7) - x^{3} - \frac{63}{2} x^{2} + \frac{21 x ^{2}}{2} + 63 x^{2} ln (x + 7) - 147 x + 441 x ln (x + 7) + 1029 ln ∣ x + 7 ∣ + \frac{9261}{2} - 3087 + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \int (x + 7)^{2} ln (x + 7) d x

Multipliziere aus

(x + 7)^{2} ln (x + 7) : x^{2} ln (x + 7) + 14 x ln (x + 7) + 49 ln (x + 7)

= 9 \cdot \int x^{2} ln (x + 7) + 14 x ln (x + 7) + 49 ln (x + 7) 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

= 9 (\int x^{2} ln (x + 7) d x + \int 14 x ln (x + 7) d x + \int 49 ln (x + 7) d x)

\int x^{2} ln (x + 7) d x = \frac{1}{3} x^{3} ln (x + 7) - \frac{1}{3} (\frac{x ^{3}}{3} - \frac{7 x ^{2}}{2} + 49 x - 343 ln ∣ x + 7 ∣)

\int 14 x ln (x + 7) d x = 14 (ln (x + 7) (\frac{1}{2} (x + 7)^{2} - 7 (x + 7)) - \frac{1}{4} (x^{2} - 14 x - 147))

\int 49 ln (x + 7) d x = 49 (x ln (x + 7) + 7 ln (x + 7) - x - 7)

= 9 (\frac{1}{3} x^{3} ln (x + 7) - \frac{1}{3} (\frac{x ^{3}}{3} - \frac{7 x ^{2}}{2} + 49 x - 343 ln ∣ x + 7 ∣) + 14 (ln (x + 7) (\frac{1}{2} (x + 7)^{2} - 7 (x + 7)) - \frac{1}{4} (x^{2} - 14 x - 147)) + 49 (x ln (x + 7) + 7 ln (x + 7) - x - 7))

Vereinfache

9 (\frac{1}{3} x^{3} ln (x + 7) - \frac{1}{3} (\frac{x ^{3}}{3} - \frac{7 x ^{2}}{2} + 49 x - 343 ln ∣ x + 7 ∣) + 14 (ln (x + 7) (\frac{1}{2} (x + 7)^{2} - 7 (x + 7)) - \frac{1}{4} (x^{2} - 14 x - 147)) + 49 (x ln (x + 7) + 7 ln (x + 7) - x - 7)) : 3 x^{3} ln (x + 7) - x^{3} - \frac{63}{2} x^{2} + \frac{21 x ^{2}}{2} + 63 x^{2} ln (x + 7) - 147 x + 441 x ln (x + 7) + 1029 ln ∣ x + 7 ∣ + \frac{9261}{2} - 3087

= 3 x^{3} ln (x + 7) - x^{3} - \frac{63}{2} x^{2} + \frac{21 x ^{2}}{2} + 63 x^{2} ln (x + 7) - 147 x + 441 x ln (x + 7) + 1029 ln ∣ x + 7 ∣ + \frac{9261}{2} - 3087

Füge eine Konstante zur Lösung hinzu

= 3 x^{3} ln (x + 7) - x^{3} - \frac{63}{2} x^{2} + \frac{21 x ^{2}}{2} + 63 x^{2} ln (x + 7) - 147 x + 441 x ln (x + 7) + 1029 ln ∣ x + 7 ∣ + \frac{9261}{2} - 3087 + C

Graph

Beliebte Beispiele

integral of (7x+6)/(x^9)

\int \frac{7 x + 6}{x ^{9}} d x

integral of (x^3-x)/((x^4-2x^2+3)^2)

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

integral of 2t^{-4}

\int 2 t^{- 4} d t

derivative of x^6-3x^5+10x^3-15x^2+9x-2

\frac{d}{d x} (x^{6} - 3 x^{5} + 10 x^{3} - 15 x^{2} + 9 x - 2)

integral of x^3sqrt(49-x^2)

\int x^{3} 49 - x^{2} d x