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

Lösung

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

ln (3) + 8

Dezimale

9.09861 \dots

Schritte zur Lösung

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

Multipliziere aus

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

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

\int_{1}^{3} x d x = 4

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

\int_{1}^{3} \frac{1}{x} d x = ln (3)

= 4 + 4 + ln (3)

Vereinfache

= ln (3) + 8

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

\int_{- 1}^{0} e^{x} d x

\int_{\frac{1}{4}}^{2} \frac{ln ( x )}{x} d x

\int_{3}^{8} ln (1 + x) d x

\int_{0}^{\frac{π}{4}} (sec (x))^{2} d x