Final answer to the problem
$\frac{x^{5}}{5}+\frac{x^{3}a^2}{3}+9x+\frac{1}{2}ax^{4}-2x^{3}-3ax^2+C_0$
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Step-by-step Solution
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1
Rewrite the integrand $\left(x^2+ax-3\right)^2$ in expanded form
$\int\left(x^{4}+a^2x^2+9+2x^{3}a-6x^2-6ax\right)dx$
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$\int\left(x^{4}+a^2x^2+9+2x^{3}a-6x^2-6ax\right)dx$
Learn how to solve differential calculus problems step by step online. Find the integral int((x^2+ax+-3)^2)dx. Rewrite the integrand \left(x^2+ax-3\right)^2 in expanded form. Expand the integral \int\left(x^{4}+a^2x^2+9+2x^{3}a-6x^2-6ax\right)dx into 6 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^{4}dx results in: \frac{x^{5}}{5}. The integral \int a^2x^2dx results in: \frac{x^{3}a^2}{3}.
Final answer to the problem
$\frac{x^{5}}{5}+\frac{x^{3}a^2}{3}+9x+\frac{1}{2}ax^{4}-2x^{3}-3ax^2+C_0$