Evaluate
\frac{298}{5}=59.6
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\int 1+9x^{4}\mathrm{d}x
Evaluate the indefinite integral first.
\int 1\mathrm{d}x+\int 9x^{4}\mathrm{d}x
Integrate the sum term by term.
\int 1\mathrm{d}x+9\int x^{4}\mathrm{d}x
Factor out the constant in each of the terms.
x+9\int x^{4}\mathrm{d}x
Find the integral of 1 using the table of common integrals rule \int a\mathrm{d}x=ax.
x+\frac{9x^{5}}{5}
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}. Multiply 9 times \frac{x^{5}}{5}.
2+\frac{9}{5}\times 2^{5}-\left(0+\frac{9}{5}\times 0^{5}\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.
\frac{298}{5}
Simplify.
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