integral from 1 to 3 of (15+2x^3)/(x^4)

Lösung

\int_{1}^{3} \frac{15 + 2 x ^{3}}{x ^{4}} d x

\frac{130}{27} + 2 ln (3)

Dezimale

7.01203 \dots

Schritte zur Lösung

\int_{1}^{3} \frac{15 + 2 x ^{3}}{x ^{4}} d x

Multipliziere aus

\frac{15 + 2 x ^{3}}{x ^{4}} : \frac{15}{x ^{4}} + \frac{2}{x}

= \int_{1}^{3} \frac{15}{x ^{4}} + \frac{2}{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} \frac{15}{x ^{4}} d x + \int_{1}^{3} \frac{2}{x} d x

\int_{1}^{3} \frac{15}{x ^{4}} d x = \frac{130}{27}

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

= \frac{130}{27} + 2 ln (3)

\int_{0}^{2} 1 - ∣ x - 1 ∣ d x

\int_{0}^{\frac{π}{2}} cos (x) \cdot sin (x) d x

\int_{\frac{π}{6}}^{\frac{π}{3}} tan (x) sec^{2} (x) d x

\int_{0}^{2} cos (x - 2) d x

\int_{0}^{π} - 3 sin (t) cos (t) d t