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$\int\left(1200\cdot \frac{1}{500}e^{\frac{1}{500}\left(x-10\right)^3}\left(x-10\right)^3+1200\right)dx$
Learn how to solve problems step by step online. Integrate the function 1200*1/500e^(1/500(x-10)^3)(x-10)^3+1200. Find the integral. Simplifying. Expand the integral \int\left(\frac{12}{5}e^{\frac{1}{500}\left(x-10\right)^3}\left(x-10\right)^3+1200\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{12}{5}e^{\frac{1}{500}\left(x-10\right)^3}\left(x-10\right)^3dx 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 x-10 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.