Find ∫ ( 2x^4 - 4x^(-0.5) + 3 ) dx

When integrating, you need to add one to the power and divide the term by the power. We will consider each term individually, 2x⁴ will become (2x⁴⁺¹)/(4+1) = (2x⁵)/5, -4x^-0.5 will become (-4x^-0.5+1)/(-0.5+1) = (-4x^0.5)/(0.5) = -8x^0.5 and 3 = 3x⁰ will become (3x⁰⁺¹)/(0+1) = 3x. Therefore, ∫ ( 2x^4 - 4x^(-0.5) + 3 ) dx = (2x⁵)/5 -8x^0.5 + 3x + C, where C is a constant of integration. Since integration and differentiation are the inverse of each other, the C appears because there could have been a number which became zero when the formula was differentiated. Therefore, we must include a constant C when integrating. You can check your answer because differentiating the answer will give you the formula within the integral.