Evaluate
3\sin(u)-10\cos(u)+С
Differentiate w.r.t. u
3\cos(u)+10\sin(u)
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\int 10\sin(u)\mathrm{d}u+\int 3\cos(u)\mathrm{d}u
Integrate the sum term by term.
10\int \sin(u)\mathrm{d}u+3\int \cos(u)\mathrm{d}u
Factor out the constant in each of the terms.
-10\cos(u)+3\int \cos(u)\mathrm{d}u
Use \int \sin(u)\mathrm{d}u=-\cos(u) from the table of common integrals to obtain the result. Multiply 10 times -\cos(u).
-10\cos(u)+3\sin(u)
Use \int \cos(u)\mathrm{d}u=\sin(u) from the table of common integrals to obtain the result.
-10\cos(u)+3\sin(u)+С
If F\left(u\right) is an antiderivative of f\left(u\right), then the set of all antiderivatives of f\left(u\right) is given by F\left(u\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.
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