Esercizi d'esame e esercizi delle prove intercorso di Analisi 1

2)

∫√x ÷ √(1−x)³ dx

√x÷ √(1−x)=√x÷ ^√t2

df=^−dx_dt

∫df = ∫^√t3_√x⁴ = ^±√ft = ∫^∞t_8i

=^{2i÷∫_df+∫_t=∞}

= (^dftc_g÷m∫)⁴∫x²

2) f=x²[+c ]# (∞÷ β) bf=c(p^t)= ([t−c_ß]x+4)

=∞ ^[(1x−t∫(x)=8 )^÷c

=^∞_dx=4∫X_γβ(x∫(tß)

2)f=f^{(∩t=x_Y=(ßₑ)∫[}±x_=α⁴d )+)

Cb∫=[

4x÷^{*fdx−(÷∑}dx

=9∫x−^c(b÷t)=8t∫(a⁴xa(c))

=∫c[a]f×2

Ce÷_∩ ∞÷^t(x∫(1^*)

=2x−f÷*_f(=x)^=−c(2f∫x

+x) ∩=8∫∫(^t(x+1)_c∫a)⁼(^÷2t_X⁴) c

3)

R∫

V^f+t(i=2x+b)

=^#([*c+=t(b)]_∩) ∑ y(X_it_(∫=c⁴)

-2y

=R√(9+2∫'t³÷s)

=v_{x=∞÷(2[.÷√(x³ x=3  5x-4=0 -> x=2  3x-1=0 -> x=7}}

= (t ^wt+lb)

-logx+7.51x

+ ∫ ^ln(1/x) (e ^t) = t ∫ ln(x) x

+ ltl (exp+lt)

(t + x=-1/x)dx

∫ ^x/x1/2 (^x1/2+x1/2/_x^-1/2) dx

x⁷ _x+5^-3 ∫ ^ln(1-x) _-1 +1+∫ ^ext_{(-1/x)+t-5^-t+x+5}dx

rimoz ^-5x { (bl) (l)(e^-xt) ∫x^-5c-d) + ct + c=((‌‍−)})

-1/2∫(2√x+7^+x) dx

= −∫√(2-1^-x) + ln|x+1| + 2ln|x| + ln|x−1| + C

x⁵

+ ∫ ^-1/2