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Solve the following.
Evaluate: ∫ (x³ + 5x² + 4x + 1)/(x²) dx.
Evaluate: $\int \frac{x^3 + 5x^2 + 4x + 1}{x^2} \, dx$.
Answer
Answer
Integral: $\int \left(\frac{x^3+5x^2+4x+1}{x^2}\right) dx$
$\int \frac{x^3+5x^2+4x+1}{x^2}dx = \int \left(x + 5 + \frac{4}{x} + x^{-2}\right)dx$
$= \frac{x^2}{2} + 5x + 4\ln|x| - \frac{1}{x} + C$
Final answer: $\frac{x^2}{2} + 5x + 4\ln|x| - \frac{1}{x}$