Solving: $\int\sqrt{\left(y+2\right)^2+1}dy$
Exercise
$\int\sqrt{\left(y+2\right)^2+1}dx$
Step-by-step Solution
Learn how to solve integration by trigonometric substitution problems step by step online. Integrate int(((y+2)^2+1)^(1/2))dy. We can solve the integral \int\sqrt{\left(y+2\right)^2+1}dy by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dy, we need to find the derivative of y. We need to calculate dy, we can do that by deriving the equation above. Substituting in the original integral, we get. Simplifying.
Integrate int(((y+2)^2+1)^(1/2))dy
Final answer to the exercise
$\frac{\left(y+2\right)\sqrt{\left(y+2\right)^2+1}}{2}+\frac{1}{2}\ln\left|\sqrt{\left(y+2\right)^2+1}+y+2\right|+C_0$