Question - Solving an Integral Step by Step
Solution:
The image shows an integral that needs to be solved. Let's solve the integral step by step:The integral is $$ \int (8x^3 - x^2 + 5x - 1) \,dx $$.To solve it, we will integrate each term separately:1. The integral of $$ 8x^3 $$ with respect to x is $$ \frac{8}{4}x^4 $$ or $$ 2x^4 $$.2. The integral of $$ -x^2 $$ with respect to x is $$ -\frac{1}{3}x^3 $$.3. The integral of $$ 5x $$ with respect to x is $$ \frac{5}{2}x^2 $$.4. The integral of $$ -1 $$ with respect to x is $$ -x $$.Putting it all together, we get:\[ \int (8x^3 - x^2 + 5x - 1) \,dx = 2x^4 - \frac{1}{3}x^3 + \frac{5}{2}x^2 - x + C \]where $$ C $$ is the constant of integration.
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