Exercise
$\int\frac{3}{3x^2+2}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int(3/(3x^2+2))dx. The integral of a function times a constant (3) is equal to the constant times the integral of the function. Solve the integral applying the substitution u^2=\frac{3x^2}{2}. Then, take the square root of both sides, simplifying we have. 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 finding the derivative of the equation above. Isolate dx in the previous equation.
Find the integral int(3/(3x^2+2))dx
Final answer to the exercise
$\frac{3\sqrt{\frac{2}{3}}\arctan\left(\frac{\sqrt{3}x}{\sqrt{2}}\right)}{2}+C_0$