Question

Evaluate: $\int \frac{dx}{x\sqrt{4x+9}}$. (Hint: Substitute($u = \sqrt{4x+9}$)). $\frac{1}{6} \arctan(\frac{\sqrt{4x+9}}{3}) + C$ $\frac{1}{3} \ln|4x| + C$ $\frac{1}{3} \ln|\frac{\sqrt{4x+9}+3}{\sqrt{4x+9}-3}| + C$ $\frac{1}{3} \ln|\frac{\sqrt{4x+9}-3}{\sqrt{4x+9}+3}| + C$ $\frac{1}{3} x \ln\sqrt{4x+9} + C$ None of the answers presented here

          Evaluate: $\int \frac{dx}{x\sqrt{4x+9}}$. (Hint: Substitute($u = \sqrt{4x+9}$)).
$\frac{1}{6} \arctan(\frac{\sqrt{4x+9}}{3}) + C$
$\frac{1}{3} \ln|4x| + C$
$\frac{1}{3} \ln|\frac{\sqrt{4x+9}+3}{\sqrt{4x+9}-3}| + C$
$\frac{1}{3} \ln|\frac{\sqrt{4x+9}-3}{\sqrt{4x+9}+3}| + C$
$\frac{1}{3} x \ln\sqrt{4x+9} + C$
None of the answers presented here

Evaluate: ∫(dx)/(x√(4x+9)). (Hint: Substitute(u = √(4x+9))).
(1)/(6)arctan((√(4x+9))/(3)) + C
(1)/(3)ln|4x| + C
(1)/(3)ln|(√(4x+9)+3)/(√(4x+9)-3)| + C
(1)/(3)ln|(√(4x+9)-3)/(√(4x+9)+3)| + C
(1)/(3) x ln√(4x+9) + C
None of the answers presented here

Added by George G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Rukhmani Jain

06/13/2021

Step 1

Then du = 2/√4x + 9 dx. Show more…

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Evaluate: $$\int \frac{dx}{x\sqrt{4x+9}}.$$ (Hint: Substitute(u = √4x + 9).) $$\frac{1}{6}arctan\left(\frac{\sqrt{4x+9}}{3}\right)+C$$ $$\frac{1}{3}ln|4x|+C$$ $$\frac{1}{3}ln\left|\frac{\sqrt{4x+9}+3}{\sqrt{4x+9}-3}\right|+C$$ $$\frac{1}{3}ln\left|\frac{\sqrt{4x+9}-3}{\sqrt{4x+9}+3}\right|+C$$ $$\frac{1}{3}xln\sqrt{4x+9}+C$$ None of the answers presented here