∫ bˣ dx
To integrate the function ∫ bˣ dx, where b is a constant, you can use the power rule of integration for exponential functions
To integrate the function ∫ bˣ dx, where b is a constant, you can use the power rule of integration for exponential functions. The power rule states that if you have an integrand of the form ∫ x^n dx, where n is any constant except -1, the result is (x^(n+1))/(n+1) + C, where C is the constant of integration.
Applying the power rule to ∫ bˣ dx, we can rewrite the integral as follows:
∫ bˣ dx = (1/ln(b)) * (bˣ) + C
Here, we use the fact that the derivative of bˣ with respect to x is (bˣ) * ln(b), so we introduce the reciprocal of ln(b) to cancel out the derivative.
Therefore, the result of integrating ∫ bˣ dx is (1/ln(b)) * (bˣ) + C, where C is the constant of integration.
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