Skip to main content
Evaluate
Tick mark Image

Similar Problems from Web Search

Share

\int x^{3}-\frac{1}{x}\mathrm{d}x
Evaluate the indefinite integral first.
\int x^{3}\mathrm{d}x+\int -\frac{1}{x}\mathrm{d}x
Integrate the sum term by term.
\int x^{3}\mathrm{d}x-\int \frac{1}{x}\mathrm{d}x
Factor out the constant in each of the terms.
\frac{x^{4}}{4}-\int \frac{1}{x}\mathrm{d}x
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{3}\mathrm{d}x with \frac{x^{4}}{4}.
\frac{x^{4}}{4}-\ln(|x|)
Use \int \frac{1}{x}\mathrm{d}x=\ln(|x|) from the table of common integrals to obtain the result.
\frac{5^{4}}{4}-\ln(|5|)-\left(\frac{1^{4}}{4}-\ln(|1|)\right)
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
156-\ln(5)
Simplify.