integral of 1/3 sin(x-3)+e^{x+3}+x^{-3}

Lösung

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

\frac{1}{3} (x sin (x - 3) + x sin (3 - x) - cos (3 - x)) + e^{3 + x} - \frac{1}{2 x ^{2}} + C

Schritte zur Lösung

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

\int \frac{1}{3} sin (x - 3) d x = \frac{1}{3} (x sin (x - 3) + x sin (3 - x) - cos (3 - x))

\int e^{x + 3} d x = e^{3 + x}

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

= \frac{1}{3} (x sin (x - 3) + x sin (3 - x) - cos (3 - x)) + e^{3 + x} - \frac{1}{2 x ^{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} (x sin (x - 3) + x sin (3 - x) - cos (3 - x)) + e^{3 + x} - \frac{1}{2 x ^{2}} + C

x \to 0 lim ((2 + x)^{3} - 8)

\int \frac{2 x - 1}{x ^{2} + 4 x + 5} d x

\int x \cdot e^{\frac{x ^{2}}{2}} d x

d er i v a t i v e - 9 e^{x} sin (x) + 9 e^{x} cos (x)

\int \frac{1}{x 1 - ln ^{2} ( x )} d x