integral of sin(0.01x)+x^3

Lösung

\int sin (0.01 x) + x^{3} d x

- 100 cos (0.01 x) + 0.25 x^{4} + C

Schritte zur Lösung

\int sin (0.01 x) + x^{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 sin (0.01 x) d x + \int x^{3} d x

\int sin (0.01 x) d x = - 100 cos (0.01 x)

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

= - 100 cos (0.01 x) + \frac{x ^{4}}{4}

Vereinfache

= - 100 cos (0.01 x) + 0.25 x^{4}

Füge eine Konstante zur Lösung hinzu

= - 100 cos (0.01 x) + 0.25 x^{4} + C

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

\int \frac{sec ^{2} ( x ) + sec ^{5} ( x )}{cot ( x )} d x

\int \frac{1}{x ^{2} + 8 - 6 x} d x

\int \frac{1}{3 - 4 t ^{2}} d t

\int 1 0^{- 8} d x