Final Answer
$\ln\left(x\right)+\frac{1}{-3x^{3}}+C_0$
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Step-by-step Solution
Problem to solve:
$\int\frac{x^3+1}{x^4}dx$
Specify the solving method
1
Expand the fraction $\frac{x^3+1}{x^4}$ into $2$ simpler fractions with common denominator $x^4$
$\int\left(\frac{x^3}{x^4}+\frac{1}{x^4}\right)dx$
Learn how to solve integrals of rational functions problems step by step online.
$\int\left(\frac{x^3}{x^4}+\frac{1}{x^4}\right)dx$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^3+1)/(x^4))dx. Expand the fraction \frac{x^3+1}{x^4} into 2 simpler fractions with common denominator x^4. Simplify the resulting fractions. Expand the integral \int\left(\frac{1}{x}+\frac{1}{x^4}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{x}dx results in: \ln\left(x\right).
Final Answer
$\ln\left(x\right)+\frac{1}{-3x^{3}}+C_0$