Question - Solving Indefinite Integral of Polynomial Expression
Solution:
The image shows the integral of a polynomial expression. I'll guide you through the steps to solve the indefinite integral:∫(8x^3 - x^2 + 5x - 1)dxTo integrate this polynomial term by term, you would use the power rule for integration. The power rule states that the integral of x^n dx is (1/(n+1)) * x^(n+1) + C, where C is the constant of integration.Applying this rule to each term, you would get:∫8x^3 dx = 8 * ∫x^3 dx = 8 * (1/4) * x^4 = 2x^4∫(-x^2) dx = (-1) * ∫x^2 dx = (-1) * (1/3) * x^3 = -1/3x^3∫5x dx = 5 * ∫x dx = 5 * (1/2) * x^2 = 5/2x^2∫(-1) dx = -1 * ∫dx = -1 * x = -xAdding them all together, you get:2x^4 - 1/3x^3 + 5/2x^2 - x + CTherefore, the integral of the given expression is:2x^4 - 1/3x^3 + 5/2x^2 - x + C
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