integral of (pi/(x^4)+e^2sqrt(x))

Lösung

\int (\frac{π}{x ^{4}} + e^{2} x) d x

- \frac{π}{3 x ^{3}} + e^{2} \frac{2}{3} x^{\frac{3}{2}} + C

Schritte zur Lösung

\int \frac{π}{x ^{4}} + e^{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 \frac{π}{x ^{4}} d x + \int e^{2} x d x

\int \frac{π}{x ^{4}} d x = - \frac{π}{3 x ^{3}}

\int e^{2} x d x = e^{2} \frac{2}{3} x^{\frac{3}{2}}

= - \frac{π}{3 x ^{3}} + e^{2} \frac{2}{3} x^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= - \frac{π}{3 x ^{3}} + e^{2} \frac{2}{3} x^{\frac{3}{2}} + C

\int x cosh (a x) d x

\int \frac{a}{2 x} d x

\int \frac{3 x}{1 - 4 x ^{2}} d x

\int \frac{cos ( x )}{2 - sin ^{2} ( x )} d x

\int \frac{2 x ^{\frac{3}{2}}}{3 x} d x