Final answer:
To evaluate the integral ∫(2√[x⁴]-x⁻³) dx, simplify the expression and integrate each term separately to find (2/3)x³ - (1/2)x⁻² + C.
Step-by-step explanation:
To evaluate the integral ∫(2√[x⁴]-x⁻³) dx, we can simplify the expression under the integral sign. The square root of x⁴ can be written as x², and x⁻³ can be written as 1/x³. So, we have ∫(2x²-1/x³) dx.
Next, we integrate each term separately. The integral of 2x² is (2/3)x³, and the integral of 1/x³ is (-1/2)x⁻².
Finally, we can combine the results to obtain the final answer: (2/3)x³ - (1/2)x⁻² + C, where C is the constant of integration.