Final answer to the problem
$\sqrt{255+x^2}-\sqrt{\left(x-20\right)^2+100}-40\ln\left(\sqrt{\left(x-20\right)^2+100}+x-20\right)+C_1$
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Step-by-step Solution
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Find the integral
$\int\left(\frac{x}{\sqrt{255+x^2}}+\frac{-\left(20+x\right)}{\sqrt{500-40x+x^2}}\right)dx$
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$\int\left(\frac{x}{\sqrt{255+x^2}}+\frac{-\left(20+x\right)}{\sqrt{500-40x+x^2}}\right)dx$
Learn how to solve problems step by step online. Find the integral of x/((255+x^2)^1/2)+(-(20+x))/((500-40xx^2)^1/2). Find the integral. Simplify the expression inside the integral. The integral \int\frac{x}{\sqrt{255+x^2}}dx results in: \sqrt{255+x^2}. The integral \int\frac{-20-x}{\sqrt{500-40x+x^2}}dx results in: -\int\frac{20+x}{\sqrt{500-40x+x^2}}dx.
Final answer to the problem
$\sqrt{255+x^2}-\sqrt{\left(x-20\right)^2+100}-40\ln\left(\sqrt{\left(x-20\right)^2+100}+x-20\right)+C_1$