integral of ((4x-1))/((2x+1)^{3/2)}

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\int 10 csc^{2} (- 5 x) cot^{4} (- 5 x) d x

\int \frac{cos ( 2 x ) + sin ^{2} ( x )}{2 cos ( x )} d x

\int 6 x^{2} (3 - 2 x^{3})^{3} d x

\int (\frac{x ^{3}}{3} - \frac{x ^{4}}{2} + \frac{x ^{5}}{5}) d x

\int \frac{1}{x + 3 x - 4} d x