Find ∫(2x^5 - 1/(4x^3) - 5)dx giving each term in its simplest form.
Firstly, we can rewrite 1/(4x3) as 1/4 x-3. Therefore, I can write the integral as a sum of integrals ∫(2x5 - 1/(4x3) - 5)dx=2 ∫x5dx-1/4 ∫x-3 dx-5 ∫dx. Using the general formula: ∫ xndx=xn+1/(n+1) + C for all real n, n not equal to -1, we have: ∫x5 dx= x6/6 + C, ∫ x-3 dx= x-2/-2 + C and ∫x0 dx=x1/1 + C. So, ∫(2x5 - 1/(4x3) - 5)dx = 2/6 x6-1/(-2)4 x-2 - 5x +C=x6/3+1/(8x2)- 5x+C.
