INTEGRALI INDEFINITI / ESERCIZI PROPOSTI
INTEGRALI INDEFINITI / ESERCIZI PROPOSTI
INTEGRALI INDEFINITI / ESERCIZI PROPOSTI
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4 M.GUIDA, S.ROLANDO<br />
i*)<br />
l)<br />
m)<br />
n)<br />
o)<br />
p)<br />
q)<br />
r)<br />
s)<br />
t)<br />
u*)<br />
<br />
1<br />
√<br />
e<br />
−2x<br />
− 1 dx..............................................................[arcsin (ex )+c]<br />
<br />
1<br />
dx...........................................................[log |1+logx| + c]<br />
x + x log x<br />
<br />
log x<br />
<br />
<br />
x 4+3log 2 x dx. ................................................... 1<br />
3<br />
4+3log 2 x + c<br />
log x<br />
√ dx. ............................................................. [2 √ x (log x − 2) + c]<br />
x<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
sin 2 xdx. ................................................................ x−sin x cos x<br />
2<br />
+ c <br />
<br />
<br />
sin 3 cos<br />
xdx. ..............................................................<br />
3 x<br />
3<br />
− cos x + c<br />
1<br />
dx. ..............................................................[log |tan x| + c]<br />
sin x cos x<br />
1<br />
sin 2 dx. .........................................................[tan x − cot x + c]<br />
x cos 2 x<br />
cos x<br />
<br />
3 − cos 2 x dx. ...................................................... 1√ sin x<br />
2<br />
arctan √<br />
2<br />
+ c<br />
4sinx<br />
4cos 2 dx. .......................................[−2arctan(2cosx − 2) + c]<br />
x − 8cosx +5<br />
<br />
<br />
x<br />
x arctan (1 + 16x) dx..............<br />
2<br />
1<br />
2<br />
arctan (1 + 16x)+<br />
512 log 1+(1+16x) 2 <br />
− x 32 + c<br />
9. Per ciascuna delle seguenti funzioni definite a tratti (continue sul proprio dominio), calcolare tutte<br />
le primitive F (x) e determinare quella che vale 1 in x 0 =0:<br />
⎧<br />
⎨ x +2<br />
<br />
se x1<br />
<br />
log 1+25x<br />
2<br />
se x ≤ 1<br />
c) f (x) =<br />
x log 26 se x>1<br />
<br />
x log 1+25x<br />
2<br />
− 2x + 2 5<br />
arctan 5x + c se x ≤ 1<br />
...................... F (x) =<br />
log 26<br />
2<br />
x 2 + c se x>1 ,c=1<br />
⎧<br />
⎨ 4x +1 se x ≤ 0<br />
d) f (x) = 1<br />
⎩ √ se 0