Gemakkelijk?

kotje

a)

\(\int3^{\sqrt{2x+1}} dx=\)

b) Bewijs:

\(\int\sec{\theta} d\theta=\ln\vert\sec{\theta}+\tan{\theta}\vert+C\)

PeterPan

kotje schreef:a)
\(\int3^{\sqrt{2x+1}} dx=\)

b) Bewijs:
\(\int\sec{\theta} d\theta=\ln\vert\sec{\theta}+\tan{\theta}\vert+C\)

a.)

\(\int3^{\sqrt{2x+1}} dx=\)

(stel y =

\(\sqrt{2x+1}\)

, dan is x = y²/2-1/2 en dus dx = ydy)

\(\int y\cdot 3^{y} dy= \frac{y\cdot 3^{y}}{\ln(3)} - \frac{3^y}{\ln^2(3)} \)

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