Is this antiderivative ok?

Question

derivative:

f(x)=7x^6 - 8/x^3 + 3(sq root of x)


antiderivative:

x^7 + 4/x^2 + 3/2x + C

Answer 1

I = ∫ 7x^6 dx - 8 ∫ x^(-3) dx + 3 ∫ x^(1/2) dx
I = x^7 + 4 x^(- 2) + 3 x^(3/2) / (3/2) + C
I = x^7 + 4 / x ² + 2 x^(3/2) + C

Answer 2

Just the term corresponding to the square root is incorrect.

sqrt(x) = x^(1/2), and when you find an antiderivative of power (not -1), you add one to the power, then divide by the new power.

x^n -> x^(n+1)/(n+1), unless n = -1.

Answer 3

no. the 1st term is ok.( i.e. x raised to 7). the 3rd term is incorrect. (3/2x.) it should be 2 x raised to 3/2.