integral from 2 to 5 of 1/((x-2)^{-1)}

Lösung

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

\frac{9}{2}

Dezimale

4.5

Schritte zur Lösung

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

Vereinfache

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

= \int_{2}^{5} x - 2 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_{2}^{5} x d x - \int_{2}^{5} 2 d x

\int_{2}^{5} x d x = \frac{21}{2}

\int_{2}^{5} 2 d x = 6

= \frac{21}{2} - 6

Vereinfache

\frac{21}{2} - 6 : \frac{9}{2}

= \frac{9}{2}

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

\int_{\frac{π}{6}}^{\frac{π}{3}} 6 cos (x) d x

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

\int_{0}^{y^{2}} x^{2} y d x

\int_{2}^{5} \frac{1}{ln ( x )} d x