Questions: Evaluate the following indefinite integral. [ int frac14 x^4 d x ]

Solution Steps

We start with the integral

\[ \int \frac{1}{4 x^{4}} \, dx. \]

This can be rewritten as

\[ \int \frac{1}{4} x^{-4} \, dx. \]

Using the power rule for integration, we have

\[ \int x^{-4} \, dx = \frac{x^{-3}}{-3} + C = -\frac{1}{3 x^{3}} + C. \]

Thus, incorporating the constant factor \(\frac{1}{4}\), we get

\[ \int \frac{1}{4} x^{-4} \, dx = \frac{1}{4} \left(-\frac{1}{3 x^{3}} + C\right) = -\frac{1}{12 x^{3}} + C. \]

Final Answer