Exercise
$\int\left(\frac{9}{5x\sqrt{49-25x^2}}\right)dx$
Step-by-step Solution
Learn how to solve integration by trigonometric substitution problems step by step online. Find the integral int(9/(5x(49-25x^2)^(1/2)))dx. Take the constant \frac{1}{5} out of the integral. First, factor the terms inside the radical by 25 for an easier handling. Taking the constant out of the radical. We can solve the integral \frac{1}{5}\int\frac{9}{5x\sqrt{\frac{49}{25}-x^2}}dx by applying integration method of trigonometric substitution using the substitution.
Find the integral int(9/(5x(49-25x^2)^(1/2)))dx
Final answer to the exercise
$-\frac{9}{35}\ln\left|\frac{7+\sqrt{49-25x^2}}{5x}\right|+C_0$