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Beliebt Rechnen >

integral of 4^{sin(x)}cos(x)

Lösung

\int 4^{s i n (x)} cos (x) d x

Lösung

\frac{2 ^{2 s i n (x) - 1}}{ln ( 2 )} + C

Schritte zur Lösung

\int 4^{s i n (x)} cos (x) d x

Wende U-Substitution an

= \int 4^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{4 ^{u}}{ln ( 4 )}

Setze in

u = sin (x)

ein

= \frac{4 ^{s i n (x)}}{ln ( 4 )}

Vereinfache

\frac{4 ^{s i n (x)}}{ln ( 4 )} : \frac{2 ^{2 s i n (x) - 1}}{ln ( 2 )}

= \frac{2 ^{2 s i n (x) - 1}}{ln ( 2 )}

Füge eine Konstante zur Lösung hinzu

= \frac{2 ^{2 s i n (x) - 1}}{ln ( 2 )} + C

Graph

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