Question

∫$\frac {5(x^6+1)}{X+1}$dx = (where C is a constant of integration.)

• A. $\frac {5x^7}{7}$+ 5x + 5 tan-1 x + c
• B. 5 tan–1 x + log (x2 + 1) + C
• C. 5(x + 1) + log (x + 1) + C
• D. x5 – $\frac {5x^3}{3}$ + 5x + C

Answer 1

Answer: (D)

x5 – $\frac {5x^3}{3}$ + 5x + C

Answer 2

Let I = ∫$\frac {5(x^6+1)}{X+1}$dx
I = 5 ∫ $\frac {(x^2)^3+(1)^3}{X+1}$dx
I =5 ∫ $\frac {(x^2 +1) (x^4 -x^2 +1)}{(X^2+1)}$dx
I =5 ∫ (x4 -x2 +1) dx
I =5 ∫ x4 dx - 5 ∫ x2 dx + 5 ∫ 1 dx
I = 5 x $\frac {x^5}{5}$ - 5$\frac {x^3}{3}$ + 5x + C
I = x5 – $\frac {5x^3}{3}$ + 5x + C
Therefore, the correct option is (D) x5 – $\frac {5x^3}{3}$ + 5x + C