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

The integral of (4x^2-2)x is 1/16 (4x^2-2)^2+C

Popular >

integral of (4x^2-2)x

\int (4 x^{2} - 2) x d x

\frac{1}{16} (4 x^{2} - 2)^{2} + C

Solution steps

\int (4 x^{2} - 2) x d x

Apply u-substitution

: \int \frac{u}{8} d u

= \int \frac{u}{8} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{8} \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{1}{8} \cdot \frac{u ^{2}}{2}

Substitute back

u = 4 x^{2} - 2

= \frac{1}{8} \cdot \frac{( 4 x ^{2} - 2 ) ^{2}}{2}

Simplify

\frac{1}{8} \cdot \frac{( 4 x ^{2} - 2 ) ^{2}}{2} : \frac{1}{16} (4 x^{2} - 2)^{2}

= \frac{1}{16} (4 x^{2} - 2)^{2}

Add a constant to the solution

= \frac{1}{16} (4 x^{2} - 2)^{2} + C

y = sin (sin (x)), (3 π, 0)

\frac{\partial}{\partial x} (sin (x^{2} - 5 x y))

\int \frac{1}{3 x} d x

\frac{d}{d x} ((e^{(x^{2})} + 4)^{2} (4 x)^{3} x)

\int \frac{1}{sin ( x ) cos ^{3} ( x )} d x

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