Final Answer
$-x^{3}+\frac{3}{5}x^{5}-\frac{1}{3}x^{6}+x^2+C_0$
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Step-by-step Solution
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1
Find the integral
$\int\left(\left(x\cdot x^2-x^2+1\right)^2-\left(x\cdot x^2-x+1\right)^2\right)dx$
Learn how to solve integral calculus problems step by step online.
$\int\left(\left(x\cdot x^2-x^2+1\right)^2-\left(x\cdot x^2-x+1\right)^2\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral of (xx^2-x^2+1)^2-(xx^2-x+1)^2. Find the integral. Simplify the expression inside the integral. The integral \int\left(x^{3}-x^2+1\right)^2dx results in: \frac{x^{7}}{7}-\frac{1}{3}x^{6}+\frac{1}{2}x^{4}+\frac{x^{5}}{5}-\frac{2}{3}x^{3}+x. Gather the results of all integrals.
Final Answer
$-x^{3}+\frac{3}{5}x^{5}-\frac{1}{3}x^{6}+x^2+C_0$