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

Lösung

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

\frac{3}{2}

Dezimale

1.5

Schritte zur Lösung

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

\frac{1 + x ^{2}}{x ^{2}} = \frac{1}{x ^{2}} + 1

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

Wende Exponentenregel an:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{x ^{2}} = x^{- 2}

= \int_{1}^{2} x^{- 2} + 1 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}^{2} x^{- 2} d x + \int_{1}^{2} 1 d x

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

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

= \frac{1}{2} + 1

Vereinfache

\frac{1}{2} + 1 : \frac{3}{2}

= \frac{3}{2}

\int_{1}^{e} \frac{( t ^{6} + 1 )}{t} d t

\int_{1}^{2} (6 - 5 x)^{4} d x

\int_{3}^{15} \frac{1}{x} d x

\int_{1}^{8} 1 + x d x

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