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Popular Calculus >

integral of x(4x+1)

Solution

\int x (4 x + 1) d x

Solution

\frac{4 x ^{3}}{3} + \frac{x ^{2}}{2} + C

Solution steps

\int x (4 x + 1) d x

Expand

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

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

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

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

= \frac{4 x ^{3}}{3} + \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{4 x ^{3}}{3} + \frac{x ^{2}}{2} + C

Graph

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Frequently Asked Questions (FAQ)

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