Question - Solving a Polynomial Integral
mathindefinite integralsolving polynomial integralpolynomial integral solutionpower rule of integration
Solution:
The image contains an integral that you would like to solve. The integral is:∫(8x^3 - x^2 + 5x - 1) dxTo solve this integral, we integrate each term separately with respect to x:∫8x^3 dx - ∫x^2 dx + ∫5x dx - ∫1 dxNow, for each term, apply the power rule of integration, which states that ∫x^n dx = (x^(n+1))/(n+1) + C where C is the constant of integration:1. ∫8x^3 dx = (8/4)x^(3+1) = 2x^42. ∫x^2 dx = (1/3)x^(2+1) = (1/3)x^33. ∫5x dx = (5/2)x^(1+1) = (5/2)x^24. ∫1 dx = xNow, put them all together, including the different signs:2x^4 - (1/3)x^3 + (5/2)x^2 - x + CSo the final answer for the indefinite integral is:2x^4 - (1/3)x^3 + (5/2)x^2 - x + C
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