integral of (x^2)/((5x+7)^3)

Lösung

\int \frac{x ^{2}}{( 5 x + 7 ) ^{3}} d x

- \frac{x ^{2}}{10 ( 5 x + 7 ) ^{2}} + \frac{1}{5} (- \frac{x}{5 ( 5 x + 7 )} + \frac{1}{25} ln ∣ 5 x + 7 ∣) + C

Schritte zur Lösung

\int \frac{x ^{2}}{( 5 x + 7 ) ^{3}} d x

Wende die partielle Integration an

= - \frac{x ^{2}}{10 ( 5 x + 7 ) ^{2}} - \int - \frac{x}{5 ( 5 x + 7 ) ^{2}} d x

\int - \frac{x}{5 ( 5 x + 7 ) ^{2}} d x = - \frac{1}{5} (- \frac{x}{5 ( 5 x + 7 )} + \frac{1}{25} ln ∣ 5 x + 7 ∣)

= - \frac{x ^{2}}{10 ( 5 x + 7 ) ^{2}} - (- \frac{1}{5} (- \frac{x}{5 ( 5 x + 7 )} + \frac{1}{25} ln ∣ 5 x + 7 ∣))

Vereinfache

= - \frac{x ^{2}}{10 ( 5 x + 7 ) ^{2}} + \frac{1}{5} (- \frac{x}{5 ( 5 x + 7 )} + \frac{1}{25} ln ∣ 5 x + 7 ∣)

Füge eine Konstante zur Lösung hinzu

= - \frac{x ^{2}}{10 ( 5 x + 7 ) ^{2}} + \frac{1}{5} (- \frac{x}{5 ( 5 x + 7 )} + \frac{1}{25} ln ∣ 5 x + 7 ∣) + C

\int x e^{z} d z

\int (\frac{7 x + 15 y}{x ^{2} + y ^{2}}) d x

\int (sec (x))^{4} (tan (x))^{3} d x

\int \frac{5}{1 + 25 x ^{2}} d x

\int \frac{10 x}{( x ^{2} + 1 ) ^{6}} d x