Find the integral of: [e^[3ln(x)] + e^(3x)] dx
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Originally Posted by DINOCALC09 Find the integral of: [e^[3ln(x)] + e^(3x)] dx First, let's simplify the integrand: $\displaystyle e^{3ln(x)} + e^{3x} = x^3+e^{3x}$ The integral of that is: $\displaystyle \frac{x^4}{4} + \frac{e^{3x}}{3}$
for the integral of e and its power dont u multiply it by the coefficient of x (chain rule) instead of dividing?
ignore what i said above- woops, my bad. you did it right
Say we have: $\displaystyle e^{ln(x^a)}$ Obviously, it equals $\displaystyle x^a$ Also, $\displaystyle e^{ln(x^a)} = e^{aln(x)}$ Let a = 3 $\displaystyle e^{3ln(x)} = e^{ln(x)+ln(x)+ln(x)} \Rightarrow e^{ln(x)}e^{ln(x)}e^{ln(x)} = x*x*x$
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