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The integral of 10^x dx is (1/ln10)10^x + C.

To evaluate the integral of 10^x dx, we can use the formula for the integral of a constant raised to the power of x, which is (1/lna)a^x + C, where a is the constant and C is the constant of integration. In this case, a = 10, so the integral of 10^x dx is (1/ln10)10^x + C.

To verify this result, we can take the derivative of (1/ln10)10^x + C using the power rule and the chain rule. The derivative of (1/ln10)10^x is (1/ln10)10^x ln10, and the derivative of C is 0. Therefore, the derivative of (1/ln10)10^x + C is (1/ln10)10^x ln10, which is equal to 10^x ln10. This is the original integrand, so our result is correct.

In summary, the integral of 10^x dx is (1/ln10)10^x + C, where C is the constant of integration. This result can be verified by taking the derivative of the antiderivative using the power rule and the chain rule.

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