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Differentiate w.r.t. d_8
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\int \sqrt{45}d_{8}\mathrm{d}x
Evaluate the indefinite integral first.
\sqrt{45}d_{8}x
Find the integral of \sqrt{45}d_{8} using the table of common integrals rule \int a\mathrm{d}x=ax.
3\sqrt{5}d_{8}x
Simplify.
3\times 5^{\frac{1}{2}}d_{8}\times 5-3\times 5^{\frac{1}{2}}d_{8}\times 0
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.
15\sqrt{5}d_{8}
Simplify.