integral of 4x^{1/2}+2e^x+3^x-3

Lösung

\int 4 x^{\frac{1}{2}} + 2 e^{x} + 3^{x} - 3 d x

\frac{8}{3} x^{\frac{3}{2}} + 2 e^{x} + \frac{3 ^{x}}{ln ( 3 )} - 3 x + C

Schritte zur Lösung

\int 4 x^{\frac{1}{2}} + 2 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 4 x^{\frac{1}{2}} d x + \int 2 e^{x} d x + \int 3^{x} d x - \int 3 d x

\int 4 x^{\frac{1}{2}} d x = \frac{8}{3} x^{\frac{3}{2}}

\int 2 e^{x} d x = 2 e^{x}

\int 3^{x} d x = \frac{3 ^{x}}{ln ( 3 )}

\int 3 d x = 3 x

= \frac{8}{3} x^{\frac{3}{2}} + 2 e^{x} + \frac{3 ^{x}}{ln ( 3 )} - 3 x

Füge eine Konstante zur Lösung hinzu

= \frac{8}{3} x^{\frac{3}{2}} + 2 e^{x} + \frac{3 ^{x}}{ln ( 3 )} - 3 x + C

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

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\int \frac{1}{( x ^{2} + 16 )} d x