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Beliebt Rechnen >

integral of 1/(5-2x^2)

Lösung

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

Lösung

\frac{1}{2 10} (ln \frac{2}{5} x + 1 - ln \frac{2}{5} x - 1) + C

Schritte zur Lösung

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

Wende integrale Substitution an

= \int \frac{1}{10 ( 1 - u ^{2} )} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{10} \cdot \int \frac{1}{1 - u ^{2}} d u

Nutze das gemeinsame Integral :

\int \frac{1}{1 - u ^{2}} d u = \frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2}

= \frac{1}{10} (\frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2})

Setze in

u = \frac{2}{5} x

ein

= \frac{1}{10} \frac{ln \frac{2}{5} x + 1}{2} - \frac{ln \frac{2}{5} x - 1}{2}

Vereinfache

\frac{1}{10} \frac{ln \frac{2}{5} x + 1}{2} - \frac{ln \frac{2}{5} x - 1}{2} : \frac{1}{2 10} (ln \frac{2}{5} x + 1 - ln \frac{2}{5} x - 1)

= \frac{1}{2 10} (ln \frac{2}{5} x + 1 - ln \frac{2}{5} x - 1)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2 10} (ln \frac{2}{5} x + 1 - ln \frac{2}{5} x - 1) + C

Graph

Beliebte Beispiele

integral of (2x+5)/(sqrt(-x^2-6x+16))

\int \frac{2 x + 5}{- x ^{2} - 6 x + 16} d x

integral of e^{1/50 t}

\int e^{\frac{1}{50} t} d t

integral of e^{(ax+b)}

\int e^{(a x + b)} d x

integral of (x^2)/((25+x^2)^{5/2)}

\int \frac{x ^{2}}{( 25 + x ^{2} ) ^{\frac{5}{2}}} d x

integral of cos^3(y)sin^3(2y)

\int cos^{3} (y) sin^{3} (2 y) d y