find and symplify the following. Integrate ( 2x^5 - 1/(4x^3)- 5 )dx

first the second term can be split up to make integrating it easierits easier if the x³ component is separatedthis eventually simplifies the second term to (-1/4) * x^-3so now the question is integrate (2x⁵ - (1/4)x^-3 -5) dx. For the first term, when integrating, the x term increases by 1 power and then the coefficient of x is divided by that new power thus the first term becomes 1/3 x⁶. The second term, repeat the same steps as before, while watching out for multiplying minus signs.this means the integrated form of the second term is 1/8x^-2. Finally the third term, while there appears to be no x term present, this is actually not the case. There is in fact an x⁰ which is equal to 1. So - 5x⁰ = - 5. this means the third term integrates to -5x. Then each term can be combined, a '+c' must be included on the end of the final equation, as the question did not give a value that the integrated equation would be equal to. Therefore the answer is 1/3x⁶ + 1/8x^-2 -5*x + c.