integral of (8x^{3/5}-3x^{-4}+4)

Lösung

\int (8 x^{\frac{3}{5}} - 3 x^{- 4} + 4) d x

5 x^{\frac{8}{5}} + \frac{1}{x ^{3}} + 4 x + C

Schritte zur Lösung

\int 8 x^{\frac{3}{5}} - 3 x^{- 4} + 4 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 8 x^{\frac{3}{5}} d x - \int 3 x^{- 4} d x + \int 4 d x

\int 8 x^{\frac{3}{5}} d x = 5 x^{\frac{8}{5}}

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

\int 4 d x = 4 x

= 5 x^{\frac{8}{5}} - (- \frac{1}{x ^{3}}) + 4 x

Vereinfache

= 5 x^{\frac{8}{5}} + \frac{1}{x ^{3}} + 4 x

Füge eine Konstante zur Lösung hinzu

= 5 x^{\frac{8}{5}} + \frac{1}{x ^{3}} + 4 x + C

\int \frac{( 5 y + 1 )}{( 2 y ^{2} - y - 1 )} d y

\int (\frac{2 x ^{2}}{( 3 - x ^{3} ) ^{2}}) d x

\int tanh (x) ln (cosh (x)) d x

\int \frac{( ln ( x ^{2} ) ) ^{2}}{x} d x

\int cos^{3} (5 x) sin^{2} (5 x) d x