Solving the Integral of b^x with Respect to x using the Power Rule

∫ b^x dx

To solve the integral of b^x with respect to x, we can use the power rule of integration

To solve the integral of b^x with respect to x, we can use the power rule of integration. The power rule states that for any function of the form f(x) = cx^n, the integral of f(x) with respect to x is (1/(n+1))cx^(n+1) + C, where C is the constant of integration.

In this case, we can rewrite b^x as e^(ln(b^x)). Using the properties of logarithms, ln(b^x) can be simplified as xln(b). Therefore, we can rewrite the integral as:

∫ b^x dx = ∫ e^(ln(b^x)) dx = ∫ e^(xln(b)) dx

Since e^(xln(b)) can be treated as a constant with respect to x, we can rewrite the integral as:

= e^(xln(b)) / ln(b) + C

Hence, the solution to the integral of b^x dx is e^(xln(b)) / ln(b) + C, where C is the constant of integration.

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