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Step-by-step Solution
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Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
Learn how to solve integrals involving logarithmic functions problems step by step online.
$\int\frac{\frac{1}{2}\ln\left(9x\right)}{x}dx$
Learn how to solve integrals involving logarithmic functions problems step by step online. Solve the integral of logarithmic functions int(ln((9x)^1/2)/x)dx. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Take out the constant \frac{1}{2} from the integral. We can solve the integral \int\frac{\ln\left(9x\right)}{x}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 9x it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above.