integral of (3x+4)/(sqrt(4-x^2))

Lösung

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

- 3 4 - x^{2} + 4 arcsin (\frac{1}{2} x) + C

Schritte zur Lösung

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

Multipliziere aus

\frac{3 x + 4}{4 - x ^{2}} : \frac{3 x}{4 - x ^{2}} + \frac{4}{4 - x ^{2}}

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

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

\int \frac{4}{4 - x ^{2}} d x = 4 arcsin (\frac{1}{2} x)

= - 3 4 - x^{2} + 4 arcsin (\frac{1}{2} x)

Füge eine Konstante zur Lösung hinzu

= - 3 4 - x^{2} + 4 arcsin (\frac{1}{2} x) + C

\int \frac{x ^{2} - 15}{x ^{3}} d x

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

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\int \frac{e ^{2 x}}{1 + 6 e ^{2 x} + 9 e ^{2 x}} d x