# Evaluate the following integrals. \int (2x^{3}-x^{2}+3x-7)dx

Evaluate the following integrals.
$\int \left(2{x}^{3}-{x}^{2}+3x-7\right)dx$
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Step 1
To evaluate the given integrals.
Step 2
Given that
$=\int \left(2{x}^{3}-{x}^{2}+3x-7\right)dx$
$=\int 2{x}^{3}dx-\int {x}^{2}dx+\int 3xdx-\int 7dx$
$=\frac{2{x}^{4}}{4}-\frac{{x}^{3}}{3}+\frac{3{x}^{2}}{2}-7x+c$
$=\frac{{x}^{4}}{2}-\frac{{x}^{3}}{3}+\frac{3{x}^{2}}{2}-7x+c$