de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of ((3x-17))/((x^2-6x+10))

Lösung

\int \frac{( 3 x - 17 )}{( x ^{2} - 6 x + 10 )} d x

Lösung

\frac{3}{2} ln x^{2} - 6 x + 10 - 8 arctan (x - 3) + C

Schritte zur Lösung

\int \frac{3 x - 17}{x ^{2} - 6 x + 10} d x

Wende die partielle Integration an

= (3 x - 17) arctan (x - 3) - \int 3 arctan (x - 3) d x

\int 3 arctan (x - 3) d x = 3 (x arctan (x - 3) - \frac{1}{2} ln x^{2} - 6 x + 10 - 3 arctan (x - 3))

= (3 x - 17) arctan (x - 3) - 3 (x arctan (x - 3) - \frac{1}{2} ln x^{2} - 6 x + 10 - 3 arctan (x - 3))

Vereinfache

(3 x - 17) arctan (x - 3) - 3 (x arctan (x - 3) - \frac{1}{2} ln x^{2} - 6 x + 10 - 3 arctan (x - 3)) : \frac{3}{2} ln x^{2} - 6 x + 10 - 8 arctan (x - 3)

= \frac{3}{2} ln x^{2} - 6 x + 10 - 8 arctan (x - 3)

Füge eine Konstante zur Lösung hinzu

= \frac{3}{2} ln x^{2} - 6 x + 10 - 8 arctan (x - 3) + C

Graph

Beliebte Beispiele

integral of tan(θ)ln(x)sec(θ)

\int tan (θ) ln (x) sec (θ) d θ

integral of sin^4(5x)*cos^2(5x)

\int sin^{4} (5 x) \cdot cos^{2} (5 x) d x

integral of picos(nt)

\int π cos (n t) d t

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

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

integral of (4x^3-8)/(x^5)

\int \frac{4 x ^{3} - 8}{x ^{5}} d x