Find the integral $\int\frac{1}{\left(10^{-131}+x\right)^2}dx$

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$\int\frac{1}{{\left(\left(1\times 10^{-131}+x\right)\right)}^2}dx$

Learn how to solve integrals of rational functions problems step by step online. Find the integral int(1/((10^(-131)+x)^2))dx. Calculate the power 10^{-131}. We can solve the integral \int\frac{1}{{\left(\left(1\times 10^{-131}+x\right)\right)}^2}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 1\times 10^{-131}+x it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. 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 deriving the equation above. Substituting u and dx in the integral and simplify.