Final answer to the problem
$\frac{x^{\left(2a+1\right)}}{2a+1}+\frac{2x^{\left(a+1\right)}}{a+1}-80x+C_0$
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Step-by-step Solution
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1
Find the integral
$\int\left(\left(x^a\right)^1-8\right)\left(x^a+1+9\right)dx$
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$\int\left(\left(x^a\right)^1-8\right)\left(x^a+1+9\right)dx$
Learn how to solve problems step by step online. Integrate the function (x^a^1-8)(x^a+1+9). Find the integral. Simplify the expression inside the integral. Rewrite the integrand \left(x^a-8\right)\left(x^a+10\right) in expanded form. Expand the integral \int\left(x^{2a}+2x^a-80\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately.
Final answer to the problem
$\frac{x^{\left(2a+1\right)}}{2a+1}+\frac{2x^{\left(a+1\right)}}{a+1}-80x+C_0$