Skip to main content
Evaluate
Tick mark Image
Differentiate w.r.t. x
Tick mark Image

Similar Problems from Web Search

Share

\int \left(x^{2}\right)^{2}+6x^{2}+9\mathrm{d}x
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+3\right)^{2}.
\int x^{4}+6x^{2}+9\mathrm{d}x
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
\int x^{4}\mathrm{d}x+\int 6x^{2}\mathrm{d}x+\int 9\mathrm{d}x
Integrate the sum term by term.
\int x^{4}\mathrm{d}x+6\int x^{2}\mathrm{d}x+\int 9\mathrm{d}x
Factor out the constant in each of the terms.
\frac{x^{5}}{5}+6\int x^{2}\mathrm{d}x+\int 9\mathrm{d}x
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{4}\mathrm{d}x with \frac{x^{5}}{5}.
\frac{x^{5}}{5}+2x^{3}+\int 9\mathrm{d}x
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}. Multiply 6 times \frac{x^{3}}{3}.
\frac{x^{5}}{5}+2x^{3}+9x
Find the integral of 9 using the table of common integrals rule \int a\mathrm{d}x=ax.
9x+2x^{3}+\frac{x^{5}}{5}+С
If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.