integral from 2 to 3 of (x^4+1)/(x^5+5x)

Lösung

\int_{2}^{3} \frac{x ^{4} + 1}{x ^{5} + 5 x} d x

\frac{- 4 ln ( 21 ) + 4 ln ( 3 ) - 4 ln ( 2 ) + 4 ln ( 86 )}{20}

Dezimale

0.36305 \dots

Schritte zur Lösung

\int_{2}^{3} \frac{x ^{4} + 1}{x ^{5} + 5 x} d x

Multipliziere aus

\frac{x ^{4} + 1}{x ^{5} + 5 x} : \frac{x ^{4}}{x ^{5} + 5 x} + \frac{1}{x ^{5} + 5 x}

Wende die Summenregel an:

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

= \int_{2}^{3} \frac{x ^{4}}{x ^{5} + 5 x} d x + \int_{2}^{3} \frac{1}{x ^{5} + 5 x} d x

\int_{2}^{3} \frac{x ^{4}}{x ^{5} + 5 x} d x = \frac{1}{4} (ln (86) - ln (21))

\int_{2}^{3} \frac{1}{x ^{5} + 5 x} d x = \frac{4 ln ( 3 ) - 4 ln ( 2 ) - ln ( 86 ) + ln ( 21 )}{20}

= \frac{1}{4} (ln (86) - ln (21)) + \frac{4 ln ( 3 ) - 4 ln ( 2 ) - ln ( 86 ) + ln ( 21 )}{20}

Vereinfache

\frac{1}{4} (ln (86) - ln (21)) + \frac{4 ln ( 3 ) - 4 ln ( 2 ) - ln ( 86 ) + ln ( 21 )}{20} : \frac{- 4 ln ( 21 ) + 4 ln ( 3 ) - 4 ln ( 2 ) + 4 ln ( 86 )}{20}

= \frac{- 4 ln ( 21 ) + 4 ln ( 3 ) - 4 ln ( 2 ) + 4 ln ( 86 )}{20}

(ln (\frac{1 + x}{1 - x}))^{^{'}}

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

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

\int sec^{3} (2 x) tan (2 x) d x

d er i v a t i v e x^{2} (1 - x)^{2}