Answer
$$\int^{\pi}_0(5e^x+3\sin x)dx=5e^\pi+1$$
Work Step by Step
$$A=\int^{\pi}_0(5e^x+3\sin x)dx$$ According to Table 1, we have $$\int cf(x)dx=c\int f(x)dx$$ $$\int[f(x)+g(x)]dx=\int f(x)dx+\int g(x)dx$$ Therefore, $$A=5\int^{\pi}_0(e^x)dx+3\int^{\pi}_0(\sin x)dx$$
Also, from Table 1, $$\int (e^x)dx=e^x$$ $$\int(\sin x)dx=-\cos x$$ Therefore, $$A=5(e^x)\Bigg]^\pi_0-3\cos x\Bigg]^\pi_0$$ $$A=5(e^\pi-e^0)-3(\cos\pi-\cos0)$$ $$A=5(e^\pi-1)-3(-1-1)$$ $$A=5e^\pi-5-3\times(-2)$$ $$A=5e^\pi+1$$
