Question-216670

Question Number 216670 by ahmed2025 last updated on 15/Feb/25

Answered by shunmisaki007 last updated on 15/Feb/25

\int \cos^{- x} (π) d x = \int {(- 1)}^{- x} d x

= \int {(e^{π i})}^{- x} d x = \int e^{- π i x} d x

= \frac{1}{- π i} e^{- π i x} + C

∴ \int \cos^{- x} (π) d x = \frac{i {(- 1)}^{- x}}{π} + C ★

Answered by MrGaster last updated on 15/Feb/25

Missing \left or extra \right

Answered by Ghisom last updated on 16/Feb/25

\int {(\cos π)}^{- x} d x = \int {(- 1)}^{- x} d x =

= \int (\cos π x - i \sin π x) d x =

= \frac{1}{π} (\sin π x + i \cos π x) + C

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