integral from 0 to 2 of (2x-1)/((x+3)^2)

Lösung

\int_{0}^{2} \frac{2 x - 1}{( x + 3 ) ^{2}} d x

2 ln (5) - 2 ln (3) - \frac{14}{15}

Dezimale

0.08831 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{2 x - 1}{( x + 3 ) ^{2}} d x

Multipliziere aus

\frac{2 x - 1}{( x + 3 ) ^{2}} : \frac{2 x}{( x + 3 ) ^{2}} - \frac{1}{( x + 3 ) ^{2}}

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{2} \frac{2 x}{( x + 3 ) ^{2}} d x - \int_{0}^{2} \frac{1}{( x + 3 ) ^{2}} d x

\int_{0}^{2} \frac{2 x}{( x + 3 ) ^{2}} d x = 2 (ln (5) - ln (3) - \frac{2}{5})

\int_{0}^{2} \frac{1}{( x + 3 ) ^{2}} d x = \frac{2}{15}

= 2 (ln (5) - ln (3) - \frac{2}{5}) - \frac{2}{15}

Vereinfache

2 (ln (5) - ln (3) - \frac{2}{5}) - \frac{2}{15} : 2 ln (5) - 2 ln (3) - \frac{14}{15}

= 2 ln (5) - 2 ln (3) - \frac{14}{15}

\int_{- 1}^{8} 3 x^{2} d x

\int_{1}^{3} (3 x^{2} - x) d x

\int_{1}^{4} e^{- x} x - e^{- x} d x

\int_{- 42.25}^{0} (\frac{13}{2} x)^{2} d x

\int_{0}^{x} \frac{1}{( 1 - x ) ^{\frac{2}{3}}} d x