# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\left(\frac{1}{60^2}+\frac{4}{5}\cdot x\right)^{\frac{\left(-1\right)}{2}}dx$

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$\int\left(\frac{1}{3597}+\frac{4}{5}x\right)^{-\frac{1}{2}}dx$

Learn how to solve calculus problems step by step online. Integrate int(((1/(60^2))+(4/5)*x)^((-1/2)))dx with respect to x. Simplifying. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Solve the integral \int\frac{1}{\sqrt{\frac{1}{3597}+\frac{4}{5}x}}dx applying u-substitution. Let u and du be. Isolate dx in the previous equation.

$\frac{5}{2}\sqrt{\frac{1}{3597}+\frac{4}{5}x}+C_0$

### Problem Analysis

$\int\left(\frac{1}{60^2}+\frac{4}{5}\cdot x\right)^{\frac{\left(-1\right)}{2}}dx$

Calculus

~ 0.05 seconds