What is the integral of (2x^2+1)^2 ?

The integral of (2x^2+1)^2 is (4x^5)/5+(4x^3)/3+x+C

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integral of (2x^2+1)^2

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

\frac{4 x ^{5}}{5} + \frac{4 x ^{3}}{3} + x + C

Solution steps

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

Expand

(2 x^{2} + 1)^{2} : 4 x^{4} + 4 x^{2} + 1

= \int 4 x^{4} + 4 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 4 x^{4} d x + \int 4 x^{2} d x + \int 1 d x

\int 4 x^{4} d x = \frac{4 x ^{5}}{5}

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int 1 d x = x

= \frac{4 x ^{5}}{5} + \frac{4 x ^{3}}{3} + x

Add a constant to the solution

= \frac{4 x ^{5}}{5} + \frac{4 x ^{3}}{3} + x + C

\frac{d}{d x} (x^{2} - 1)

\int 4 x \cdot ln (x) d x

f (x) = (\frac{x + 1}{x - 3})^{2}, at x = 7

\frac{\partial}{\partial x} (x^{2} y^{2} cos (x))

\frac{\partial}{\partial x} (ln (1 + x y))

What is the integral of (2x^2+1)^2 ?
The integral of (2x^2+1)^2 is (4x^5)/5+(4x^3)/3+x+C