integral of (-4x^6+2x^5-3x^3+3)

Lösung

\int (- 4 x^{6} + 2 x^{5} - 3 x^{3} + 3) d x

- \frac{4 x ^{7}}{7} + \frac{x ^{6}}{3} - \frac{3 x ^{4}}{4} + 3 x + C

Schritte zur Lösung

\int - 4 x^{6} + 2 x^{5} - 3 x^{3} + 3 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 4 x^{6} d x + \int 2 x^{5} d x - \int 3 x^{3} d x + \int 3 d x

\int 4 x^{6} d x = \frac{4 x ^{7}}{7}

\int 2 x^{5} d x = \frac{x ^{6}}{3}

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

\int 3 d x = 3 x

= - \frac{4 x ^{7}}{7} + \frac{x ^{6}}{3} - \frac{3 x ^{4}}{4} + 3 x

Füge eine Konstante zur Lösung hinzu

= - \frac{4 x ^{7}}{7} + \frac{x ^{6}}{3} - \frac{3 x ^{4}}{4} + 3 x + C

\int \frac{3}{( x + 1 ) ^{3}} d x

\int \frac{x ( x + 2 )}{x ^{3} + 3 x ^{2} + 1} d x

\int \frac{2 ^{x}}{7 ^{x}} d x

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

\int \frac{x}{2 x + 5} d x