Question - Solving Indefinite Integral of a Polynomial Function
Solution:
The question in the image is asking for the integral of the given function with respect to x:∫(8x^3 - x^2 + 5x - 1) dxTo solve this indefinite integral, you would integrate each term separately. The integral of a sum is the sum of the integrals, so you can integrate each term individually.The integral of 8x^3 with respect to x is (8/4)x^(3+1) = 2x^4.The integral of -x^2 with respect to x is -(1/3)x^(2+1) = -1/3 x^3.The integral of 5x with respect to x is (5/2)x^(1+1) = 5/2 x^2.The integral of -1 with respect to x is -x.Putting it all together, the indefinite integral of the function is:2x^4 - (1/3)x^3 + (5/2)x^2 - x + Cwhere C is the constant of integration.
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