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Beliebt Rechnen >

integral of sqrt(1+tan(h^2)x)

Lösung

\int 1 + tan (h^{2}) x d x

Lösung

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

Schritte zur Lösung

\int 1 + tan (h^{2}) x d x

Wende U-Substitution an

= \int u cot (h^{2}) d u

Entferne die Konstante:

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

= cot (h^{2}) \cdot \int u d u

Wende die Potenzregel an

= cot (h^{2}) \frac{2}{3} u^{\frac{3}{2}}

Setze in

u = 1 + tan (h^{2}) x

ein

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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