What is the integral of (4x^2+1)^2 ?

The integral of (4x^2+1)^2 is (16x^5)/5+(8x^3)/3+x+C

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integral of (4x^2+1)^2

\int (4 x^{2} + 1)^{2} d x

\frac{16 x ^{5}}{5} + \frac{8 x ^{3}}{3} + x + C

Solution steps

\int (4 x^{2} + 1)^{2} d x

Expand

(4 x^{2} + 1)^{2} : 16 x^{4} + 8 x^{2} + 1

= \int 16 x^{4} + 8 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 16 x^{4} d x + \int 8 x^{2} d x + \int 1 d x

\int 16 x^{4} d x = \frac{16 x ^{5}}{5}

\int 8 x^{2} d x = \frac{8 x ^{3}}{3}

\int 1 d x = x

= \frac{16 x ^{5}}{5} + \frac{8 x ^{3}}{3} + x

Add a constant to the solution

= \frac{16 x ^{5}}{5} + \frac{8 x ^{3}}{3} + x + C

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What is the integral of (4x^2+1)^2 ?
The integral of (4x^2+1)^2 is (16x^5)/5+(8x^3)/3+x+C