integral from-1 to 1 of e^xcos(npix)

Lösung

\int_{- 1}^{1} e^{x} cos (nπ x) d x

\frac{e ( - 1 ) ^{n}}{π ^{2} n ^{2} + 1} - \frac{( - 1 ) ^{n}}{e ( π ^{2} n ^{2} + 1 )}

Schritte zur Lösung

\int_{- 1}^{1} e^{x} cos (nπ x) d x

Berechne das unbestimmte Integral:

\int e^{x} cos (nπ x) d x = \frac{πn e ^{x} sin ( πn x )}{π ^{2} n ^{2} + 1} + \frac{e ^{x} cos ( πn x )}{π ^{2} n ^{2} + 1} + C

Berechne die Grenzen:

\int_{- 1}^{1} e^{x} cos (nπ x) d x = \frac{e ( - 1 ) ^{n}}{π ^{2} n ^{2} + 1} - \frac{( - 1 ) ^{n}}{e ( π ^{2} n ^{2} + 1 )}

= \frac{e ( - 1 ) ^{n}}{π ^{2} n ^{2} + 1} - \frac{( - 1 ) ^{n}}{e ( π ^{2} n ^{2} + 1 )}

x \to - 3 lim (\frac{x + 3}{x ^{2} - 9})

d er i v a t i v e f (x) = 2 x e^{x}

\int (\frac{x + 5}{x ^{2} + x - 6}) d x

\int \frac{4 x}{x ^{2} - 1} d x

d er i v a t i v e f (x) = arctan (\frac{x}{2})