integral of xsqrt(1+x^2)

Lösung

\int x 1 + x^{2} d x

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

Schritte zur Lösung

\int x 1 + x^{2} d x

Wende U-Substitution an

= \int u^{2} d u

Wende die Potenzregel an

= \frac{u ^{3}}{3}

Setze in

u = 1 + x^{2}

ein

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

Vereinfache

\frac{( 1 + x ^{2} ) ^{3}}{3} : \frac{1}{3} (1 + x^{2})^{\frac{3}{2}}

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

Füge eine Konstante zur Lösung hinzu

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

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