Task/24847449
---.---.---.---.---.---
1.
∫( 4/3)*x³ -(3/2)*x² +8) dx = ( 4/3)*x⁴/4 - (3/2)*x³/3 +8x +C =x⁴/3 -x³/2 +8x +C.
---------
2. ∫sin²x*cosxdx=∫sin²xd(sinx)=(1/3)*sin³x +C.
---------
3. ∫(sinx / √cosx )dx = - ∫ (cosx)^(-1/2) d(cosx) = -2√cosx +C
π/2
∫(sinx / √cosx )dx = -2(√cosπ/2 - √cos0) = -2(0 -1) =2.
0
---------
4. ∫ (e^sinx) *cosxdx=∫ (e^sinx) d(sinx) = e^sinx +C
π/6
∫ (e^sinx) *cosxdx = e^(sinπ/6) - e^(sin0) =e^(1/2) - e^0 = √e -1 .
0