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Popular Calculus >

integral of (2x^2+1)

Solution

\int (2 x^{2} + 1) d x

Solution

\frac{2 x ^{3}}{3} + x + C

Solution steps

\int 2 x^{2} + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x^{2} d x + \int 1 d x

\int 2 x^{2} d x = \frac{2 x ^{3}}{3}

\int 1 d x = x

= \frac{2 x ^{3}}{3} + x

Add a constant to the solution

= \frac{2 x ^{3}}{3} + x + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of (2x^2+1) ?
The integral of (2x^2+1) is (2x^3)/3+x+C