Determine the following antiderivative: ∫(2x^3+1)^10x^5dx

Question

∫(2x³ + 1)¹⁰x⁵dx

Answer 1

The problem can be split into two pieces - (2x^3/10x^5) + (1/10x^5). Then reduce each piece 1/(5x^2) + 1/(10x^5).

Each piece can then be integrated using the power rule.

5x^(-2) integrates to -1/5x and the other piece to -1/(40x^4) + C