∫(ex+2x)dx=∫(ex+(eln(2))x)dx=∫(ex+ex⋅ln(2))dx=∫exdx+∫ex⋅ln(2)dx=ex+1ln(2)∫ex⋅ln(2)d(x⋅ln(2))=ex+1ln(2)⋅ex⋅ln(2)+C=ex+1ln(2)⋅(eln(2))x+C=ex+2xln(2)+C.\int(e^x+2^x)dx=\int(e^x+(e^{ln(2)})^x)dx=\\ \int(e^x+e^{x\cdot ln(2)})dx=\int e^xdx+\int e^{x\cdot ln(2)}dx=\\ e^x+\frac{1}{ln(2)}\int e^{x\cdot ln(2)}d(x\cdot ln(2))=\\ e^x+\frac{1}{ln(2)}\cdot e^{x\cdot ln(2)}+C=\\ e^x+\frac{1}{ln(2)}\cdot(e^{ln(2)})^x+C=\\ e^x+\frac{2^x}{ln(2)}+C.∫(ex+2x)dx=∫(ex+(eln(2))x)dx=∫(ex+ex⋅ln(2))dx=∫exdx+∫ex⋅ln(2)dx=ex+ln(2)1∫ex⋅ln(2)d(x⋅ln(2))=ex+ln(2)1⋅ex⋅ln(2)+C=ex+ln(2)1⋅(eln(2))x+C=ex+ln(2)2x+C.
Answer: ex+2xln(2)+C.e^x+\frac{2^x}{ln(2)}+C.ex+ln(2)2x+C.
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