integral of x^6-4x^4+x+1

Lösung

\int x^{6} - 4 x^{4} + x + 1 d x

\frac{x ^{7}}{7} - \frac{4 x ^{5}}{5} + \frac{x ^{2}}{2} + x + C

Schritte zur Lösung

\int x^{6} - 4 x^{4} + x + 1 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 x^{6} d x - \int 4 x^{4} d x + \int x d x + \int 1 d x

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

\int 4 x^{4} d x = \frac{4 x ^{5}}{5}

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

\int 1 d x = x

= \frac{x ^{7}}{7} - \frac{4 x ^{5}}{5} + \frac{x ^{2}}{2} + x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{7}}{7} - \frac{4 x ^{5}}{5} + \frac{x ^{2}}{2} + x + C

\int \frac{t ^{5}}{t ^{2} + 10} d t

\frac{d y}{d x} = 0.5 (100 - y)

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

d er i v a t i v e f (x) = x (x + 3)^{2}

y^{^{'}} - 2 y = 7