f_n (x):=∫e^((2x)/3) ((cos(x))/( (cos(x)+sin(x))^(n/3) ))dx=...? for n=1, i found f_1 (x)=(3/4)e^((2x)/3) (cos(x)+sin(x))^(2/3) + C is there any ideas for a general case or the case n=2?


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Question Number 207424 by MetaLahor1999 last updated on 14/May/24

$f_{n} (x) := \int e^{\frac{2 x}{3}} \frac{c o s (x)}{{(c o s (x) + s i n (x))}^{\frac{n}{3}}} d x = . . . ?$ $f o r n = 1, i f o u n d$ $f_{1} (x) = \frac{3}{4} e^{\frac{2 x}{3}} {(c o s (x) + s i n (x))}^{\frac{2}{3}} + C$ $i s t h e r e a n y i d e a s f o r a g e n e r a l c a s e o r$ $t h e c a s e n = 2 ?$
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