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Differentiate w.r.t. x
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\int t^{5}\mathrm{d}t
Evaluate the indefinite integral first.
\frac{t^{6}}{6}
Since \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} for k\neq -1, replace \int t^{5}\mathrm{d}t with \frac{t^{6}}{6}.
\frac{1}{6}\times \left(3x\right)^{6}-\frac{1}{6}\left(-3x\right)^{6}
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.
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Simplify.
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