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$\int15a\left(a+1\right)^3da+\int-5a\left(a+1\right)^{12}da$
Learn how to solve integral calculus problems step by step online. Find the integral int(15a(a+1)^3-5a(a+1)^2^3^2)da. Simplify the expression inside the integral. We can solve the integral \int15a\left(a+1\right)^3da 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 a+1 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 da 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. Rewriting a in terms of u.