Using linearity to evaluate a combined integral

By linearity of the definite integral, the integral of a difference is the difference of the integrals, and constant multiples can be factored out: $\int_1^5 \left[4f(x) - 2g(x)\right]dx = 4\int_1^5 f(x)\,dx - 2\int_1^5 g(x)\,dx.$

Substituting the given values $\int_1^5 f(x)dx = 8$ and $\int_1^5 g(x)dx = 3$ gives $4(8) - 2(3) = 32 - 6 = 26$. So the value of the integral is $26$.