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Beliebt Rechnen >

integral from 0 to ln(4) of (e^x)/(sqrt(e^{2x)+25)}

Lösung

\int_{0}^{l n (4)} \frac{e ^{x}}{e ^{2 x} + 25} d x

Lösung

ln (- \frac{( 4 + 41 ) ( 1 - 26 )}{25})

+1

Dezimale

0.53397 \dots

Schritte zur Lösung

\int_{0}^{l n (4)} \frac{e ^{x}}{e ^{2 x} + 25} d x

Wende U-Substitution an

= \int_{1}^{4} \frac{1}{u ^{2} + 25} d u

Trigonometrische Substitution anwenden

= \int_{a r c t a n (\frac{1}{5})}^{a r c t a n (\frac{4}{5})} sec (v) d v

Nutze das gemeinsame Integral :

\int sec (v) d v = ln ∣ tan (v) + sec (v) ∣

= [ln ∣ tan (v) + sec (v) ∣]_{a r c t a n (\frac{1}{5})}^{a r c t a n (\frac{4}{5})}

Berechne die Grenzen:

ln (\frac{4}{5} + \frac{41}{5}) - ln (\frac{1}{5} + \frac{26}{5})

= ln (\frac{4}{5} + \frac{41}{5}) - ln (\frac{1}{5} + \frac{26}{5})

Vereinfache

= ln (- \frac{( 4 + 41 ) ( 1 - 26 )}{25})

Graph

Beliebte Beispiele

limit as x approaches-infinity of 1/x+3

x \to - \infty lim (\frac{1}{x} + 3)

derivative of 4xe^{3x}

\frac{d}{d x} (4 x e^{3 x})

derivative of x/(sin(x+cos(x)))

\frac{d}{d x} (\frac{x}{sin ( x ) + cos ( x )})

derivative of e^{5x}cos(3x)

\frac{d}{d x} (e^{5 x} cos (3 x))

derivative of (x^4/(3-x^3))

\frac{d}{d x} (\frac{x ^{4}}{3 - x ^{3}})