integral of x/(sqrt(8+x^2))+3e^{4x}

Lösung

\int \frac{x}{8 + x ^{2}} + 3 e^{4 x} d x

8 + x^{2} + \frac{3}{4} e^{4 x} + C

Schritte zur Lösung

\int \frac{x}{8 + x ^{2}} + 3 e^{4 x} 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{x}{8 + x ^{2}} d x + \int 3 e^{4 x} d x

\int \frac{x}{8 + x ^{2}} d x = 8 + x^{2}

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

= 8 + x^{2} + \frac{3}{4} e^{4 x}

Füge eine Konstante zur Lösung hinzu

= 8 + x^{2} + \frac{3}{4} e^{4 x} + C

\int x^{2} ln (x^{6} - 1) d x

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d er i v a t i v e \frac{( 2 - \frac{1}{x} )}{x - 3}

\int \frac{27}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (cot (sin (x)))