Question

∫10x4+14x2+131+x2dx.

Answer 1

2x^5 +14/3x^3 + 131x +x^3/3 +С

Answer 2

We can solve this integral by distributing and integrating each term separately:

∫(10x^4 + 14x^2 + 131 + x^2) dx = ∫10x^4 dx + ∫14x^2 dx + ∫131 dx + ∫x^2 dx

Integrating each term:

= (10/5)x^5 + (14/3)x^3 + 131x + (1/3)x^3 + C = 2x^5 + (14/3)x^3 + 131x + C

where C is the constant of integration.

Therefore, the antiderivative of the function 10x^4+14x^2+131+x^2 is 2x^5+(14/3)x^3+131x+C.