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Beliebt Rechnen >

integral from 0 to 1 of 1/(e^x+e^{-x)}

Lösung

\int_{0}^{1} \frac{1}{e ^{x} + e ^{- x}} d x

Lösung

arctan (e) - \frac{π}{4}

+1

Dezimale

0.43288 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{1}{e ^{x} + e ^{- x}} d x

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= [arctan (u)]_{1}^{e}

Berechne die Grenzen:

arctan (e) - \frac{π}{4}

= arctan (e) - \frac{π}{4}

Graph

Beliebte Beispiele

derivative of-3ln(3+4x^2+5x^3-9)

\frac{d}{d x} (- 3 ln (3 + 4 x^{2}) + 5 x^{3} - 9)

d er i v a t i v e y = 6

t^2(dy)/(dt)-t=1+y+ty,y(1)=10

t^{2} \frac{d y}{d t} - t = 1 + y + t y, y (1) = 10

derivative of 6x^6

\frac{d}{d x} (6 x^{6})

integral from-35 to 0 of 1/(sqrt(1-x))

\int_{- 35}^{0} \frac{1}{1 - x} d x