Question

Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) dx x 25x2 1

Answer 1

The integral of $\int {x(25x^2 + 1)} \, dx$ is $\frac{25}{4}x^4 + \frac{x^2}{2} + C$

How to evaluate the integral?

The integral expression is given as:

$\int {x(25x^2 + 1)} \, dx$

Start by expanding the bracket

$\int {25x^3 + x} \, dx$

Next, we integrate each term in the expression

$\frac{25}{4}x^4 + \frac{x^2}{2} + C$

Hence, the integral of $\int {x(25x^2 + 1)} \, dx$ is $\frac{25}{4}x^4 + \frac{x^2}{2} + C$

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