integral of 12x^2-7x+5

Lösung

\int 12 x^{2} - 7 x + 5 d x

4 x^{3} - \frac{7 x ^{2}}{2} + 5 x + C

Schritte zur Lösung

\int 12 x^{2} - 7 x + 5 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 12 x^{2} d x - \int 7 x d x + \int 5 d x

\int 12 x^{2} d x = 4 x^{3}

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

\int 5 d x = 5 x

= 4 x^{3} - \frac{7 x ^{2}}{2} + 5 x

Füge eine Konstante zur Lösung hinzu

= 4 x^{3} - \frac{7 x ^{2}}{2} + 5 x + C

\int \frac{t}{t ^{4} + 81} d t

a re a \frac{1}{x x ^{2} - 1}, x = \frac{2}{2}, x = 2

\frac{d}{d x} ((4 x^{2} + 2 x - 5) (x^{3} + 7 x + 4))

d er i v a t i v e \frac{4 u ^{2}}{( u ^{2} + u ) ^{3}}

d er i v a t i v e f (x) = a cos (2 x) + b sin (2 x)