Integrate 2x³ + 2x/x with respect to x

Correct Answer is : 2x332x³/332x3 + 2x + k

Correct Answer is : 2x332x³/332x3 + 2x + k

Test Index

JAMB Mathematics 2016 Paper

Question : 1

Total: 50

Integrate

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

with respect to x

Solution:

Concept:

Simplify the algebraic fraction first, then integrate each term separately.

Explanation:

Rewrite the integrand by dividing each term in the numerator by

x

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

Now integrate term by term:

\int (2x^2 + 2)\,dx = \int 2x^2\,dx + \int 2\,dx.

For the first term, use the power rule:

\int 2x^2\,dx = \frac{2x^{3}}{3}.

For the second term:

\int 2\,dx = 2x.

Combine the results and add the constant of integration

k

\int \frac{2x^3 + 2x}{x}\,dx = \frac{2x^3}{3} + 2x + k.

Answer:

The correct option is C:

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

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