(x^2+ 3x + 2)^3 + log x^2
Answers
Answer:
2㏒x+(x⁶+9x⁵+33x⁴+63x³+66x²+36x+8)
Explanation:
Given that,
(x² + 3x + 2)³ + ㏒x² ↔ (1)
to make our calculation easy
factorise x² + 3x +2
⇒ x² + 3x + 2 (∵the factors of 2 are 1 & 2 to get their sum as 3)
by splitting 3x we get,
⇒ x² + 2x + x +2
⇒ x(x+2) + (x+2)
⇒ (x+2)(x+1)
Now, by substituting this in eq.(1)
⇒ ((x+2)(x+1))³ + ㏒x²
⇒ (x+2)³(x+1)³ + ㏒x²
⇒ (x³ + 2³ + 3x²(2) + 3x(2)²)(x³ + 1³ + 3x²(1) + (3x(1)²) + ㏒x²
(∵(a+b)³ = a³+b³+3a²b+3ab² & ㏒a² = 2㏒a)
⇒(x³+8+6x²+12x)(x³+3x²+3x+1) + 2㏒x
⇒(x⁶+3x⁵+3x⁴+x³+8x³+24x²+24x+8+6x⁵+18x⁴+18x³+6x²+12x⁴+36x³+36x²+12x)+2㏒x
(∵a^m × a^n = a^(m×n) )
⇒(x⁶+9x⁵+33x⁴+63x³+66x²+36x+8) + 2㏒x
HOPE THIS WOULD BE HELPFUL FOR YOU
Answer:
As you didnt mentioned anything i solved integration and differentiation for above question
