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) \cdot 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

\int_{2}^{4} (\frac{5}{x} - \frac{10}{x ^{2}}) d x

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

y^{^{'}} + a \cdot y = b

\frac{d}{d x} (2 x + 2 (cos (x) + 1) sin (x))

\int sec^{6} (3 x) tan^{2} (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