Final answer to the problem
$-\frac{1}{2}x^{6}+\frac{1}{2}x^{4}-\frac{3}{2}x^2+\frac{-2}{x}+x+C_0$
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Step-by-step Solution
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Expand the integral $\int\left(-3x^5+2x^3-3x+\frac{2}{x^2}+1\right)dx$ into $5$ integrals using the sum rule for integrals, to then solve each integral separately
$\int-3x^5dx+\int2x^3dx+\int-3xdx+\int\frac{2}{x^2}dx+\int1dx$
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$\int-3x^5dx+\int2x^3dx+\int-3xdx+\int\frac{2}{x^2}dx+\int1dx$
Learn how to solve problems step by step online. Integrate int(-3x^5+2x^3-3x2/(x^2)+1)dx. Expand the integral \int\left(-3x^5+2x^3-3x+\frac{2}{x^2}+1\right)dx into 5 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int-3x^5dx results in: -\frac{1}{2}x^{6}. The integral \int2x^3dx results in: \frac{1}{2}x^{4}. The integral \int-3xdx results in: -\frac{3}{2}x^2.
Final answer to the problem
$-\frac{1}{2}x^{6}+\frac{1}{2}x^{4}-\frac{3}{2}x^2+\frac{-2}{x}+x+C_0$