Evaluate the integral. (Use C for the constant of integration. Remember to use absolute values where appropriate.) $\int \frac{dx}{5x \ln(x) - 9x}$ Evaluate the integral. $\int_1^9 \sqrt{y} \ln(y) dy$
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Let's choose u = ln(x) and dv = 5x - 9 dx. Differentiating u, we get du = (1/x) dx. Integrating dv, we get v = (5/2)x^2 - (9/2)x^2 = (5/2 - 9/2)x^2 = (-4/2)x^2 = -2x^2. Now, we can use the formula for integration by parts: ∫ u dv = uv - ∫ v du Plugging in the Show more…
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