Evaluate
\pi \left(\sin(\theta )+5t\right)
Differentiate w.r.t. t
5\pi
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\int 5t+\sin(\theta )\mathrm{d}x
Evaluate the indefinite integral first.
\left(5t+\sin(\theta )\right)x
Find the integral of 5t+\sin(\theta ) using the table of common integrals rule \int a\mathrm{d}x=ax.
\left(5t+\sin(\theta )\right)\pi +0\left(5t+\sin(\theta )\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.
\left(5t+\sin(\theta )\right)\pi
Simplify.
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