Evaluate the indefinite integral:
\[
\int \frac{5 x^{4}-5 x}{x^{3}} d x=\square+C
\]

Answer

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Answer

The final answer is \(\boxed{\frac{5 x^{2}}{2}+\frac{5}{x}+C}\).

Steps

Step 1 ：First, we simplify the integral \(\int \frac{5 x^{4}-5 x}{x^{3}} d x\) as \(\int 5x dx - \int \frac{5}{x^2} dx\).

Step 2 ：We then integrate the first term using the power rule, and the second term as the integral of a constant times x to the power of -2, also using the power rule.

Step 3 ：The integral of the function is \(5x^2/2 + 5/x\).

Step 4 ：Finally, we add the constant of integration, C, to our final answer.

Step 5 ：The final answer is \(\boxed{\frac{5 x^{2}}{2}+\frac{5}{x}+C}\).

Evaluate the indefinite integral:\[\int \frac{5 x^{4}-5 x}{x^{3}} d x=\square+C\]

Answer

Popular Problems

Evaluate the indefinite integral:
\[
\int \frac{5 x^{4}-5 x}{x^{3}} d x=\square+C
\]