Question

Integrate: $\int e^{2x-3}+7^{4-3\frac{x}{2}}+\sin (3x-\frac{1}{2})+\cos (\frac{2}{5}x-2)dx$

Answer 1

$\int e^{2x-3}+7^{4-3\frac{x}{2}}+\sin (3x-\frac{1}{2})+\cos (\frac{2}{5}x-2)dx=\int \frac{e^{2x}}{e^3}+\int 7^4\times (7^{-\frac{3}{2}}{)}^x+\int \sin (3x-\frac{1}{2})+\int \cos (\frac{2}{5}x-2)dx=\frac{e^{2x}}{e^3}.\frac{1}{2}+7^4.\frac{(7^{-\frac{3}{2}}{)}^x}{\log \left(7^{-\frac{3}{2}}\right)}-\frac{\cos (3x-\frac{1}{2})}{3}+\frac{\sin (\frac{2}{5}x-2)}{\frac{2}{5}}=\frac{e^{2x}}{2e^3}-7^4.\frac{2(7^{-\frac{3}{2}}{)}^x}{3\log \left(7\right)}-\frac{\cos (3x-\frac{1}{2})}{3}+\frac{5\sin (\frac{2}{5}x-2)}{2}$