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Beliebt Rechnen >

integral from 0 to 1 of sinh(4x)(x^2+5)

Lösung

\int_{0}^{1} sinh (4 x) (x^{2} + 5) d x

Lösung

\frac{45 e ^{8} + 53}{64 e ^{4}} - \frac{41}{32}

+1

Dezimale

37.12324 \dots

Schritte zur Lösung

\int_{0}^{1} sinh (4 x) (x^{2} + 5) d x

Wende die partielle Integration an

= [\frac{1}{4} cosh (4 x) (x^{2} + 5) - \int \frac{1}{2} x cosh (4 x) d x]_{0}^{1}

\int \frac{1}{2} x cosh (4 x) d x = \frac{1}{2} (\frac{1}{4} x sinh (4 x) - \frac{1}{16} cosh (4 x))

= [\frac{1}{4} cosh (4 x) (x^{2} + 5) - \frac{1}{2} (\frac{1}{4} x sinh (4 x) - \frac{1}{16} cosh (4 x))]_{0}^{1}

Vereinfache

[\frac{1}{4} cosh (4 x) (x^{2} + 5) - \frac{1}{2} (\frac{1}{4} x sinh (4 x) - \frac{1}{16} cosh (4 x))]_{0}^{1} : [\frac{1}{32} (8 x^{2} cosh (4 x) - 4 x sinh (4 x) + 41 cosh (4 x))]_{0}^{1}

= [\frac{1}{32} (8 x^{2} cosh (4 x) - 4 x sinh (4 x) + 41 cosh (4 x))]_{0}^{1}

Berechne die Grenzen:

\frac{45 e ^{8} + 53}{64 e ^{4}} - \frac{41}{32}

= \frac{45 e ^{8} + 53}{64 e ^{4}} - \frac{41}{32}

Graph

Beliebte Beispiele

integral from 0 to 1 of 1/(x^2-2x-3)

\int_{0}^{1} \frac{1}{x ^{2} - 2 x - 3} d x

integral from-1 to 4 of x^2

\int_{- 1}^{4} x^{2} d x

integral from 0 to 3 of (2-x)

\int_{0}^{3} (2 - x) d x

integral from-2 to 2 of x^3+x

\int_{- 2}^{2} x^{3} + x d x

integral from 1 to 3 of 3x(x^2+5)

\int_{1}^{3} 3 x (x^{2} + 5) d x