integral of (5x+4)^2

Lösung

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

\frac{25 x ^{3}}{3} + 20 x^{2} + 16 x + C

Schritte zur Lösung

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

Multipliziere aus

(5 x + 4)^{2} : 25 x^{2} + 40 x + 16

= \int 25 x^{2} + 40 x + 16 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 25 x^{2} d x + \int 40 x d x + \int 16 d x

\int 25 x^{2} d x = \frac{25 x ^{3}}{3}

\int 40 x d x = 20 x^{2}

\int 16 d x = 16 x

= \frac{25 x ^{3}}{3} + 20 x^{2} + 16 x

Füge eine Konstante zur Lösung hinzu

= \frac{25 x ^{3}}{3} + 20 x^{2} + 16 x + C

\int x^{3} 9 - x^{2} d x

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

\int_{- 1}^{2} 3 x^{2} + 2 x + 1 d x

d er i v a t i v e cos (cos (cos (x)))

t an g e n t x^{4} - 32 x^{2} + 256