$\int\frac{\sqrt{x^2+4}}{x^4}dx$

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$x=2\tan\left(\theta \right)$

Learn how to solve equations logarithmiques problems step by step online. int(((x^2+4)^(1/2))/(x^4))dx. We can solve the integral \int\frac{\sqrt{x^2+4}}{x^4}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get. Apply the trigonometric identity: \frac{\sec\left(\theta \right)^n}{\tan\left(\theta \right)^m}=\frac{\cos\left(\theta \right)^{\left(m-n\right)}}{\sin\left(\theta \right)^m}, where x=\theta , m=4 and n=3.