What is the integral of xsqrt(3x^2-2) ?

The integral of xsqrt(3x^2-2) is 1/9 (3x^2-2)^{3/2}+C

integral of xsqrt(3x^2-2)

\int x 3 x^{2} - 2 d x

\frac{1}{9} (3 x^{2} - 2)^{\frac{3}{2}} + C

Solution steps

\int x 3 x^{2} - 2 d x

Apply u-substitution

= \int \frac{u}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int u d u

Apply the Power Rule

= \frac{1}{6} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 3 x^{2} - 2

= \frac{1}{6} \cdot \frac{2}{3} (3 x^{2} - 2)^{\frac{3}{2}}

Simplify

\frac{1}{6} \cdot \frac{2}{3} (3 x^{2} - 2)^{\frac{3}{2}} : \frac{1}{9} (3 x^{2} - 2)^{\frac{3}{2}}

= \frac{1}{9} (3 x^{2} - 2)^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{9} (3 x^{2} - 2)^{\frac{3}{2}} + C

\int t sin (t^{2}) d t

x \to 2 lim (\frac{4 - 2 x}{x - 2})

roo t s c e^{x}

3 y d y = (2 sin (2 x) - e^{x}) y d x

\frac{\partial}{\partial x} (3 x^{6} y^{2})

What is the integral of xsqrt(3x^2-2) ?
The integral of xsqrt(3x^2-2) is 1/9 (3x^2-2)^{3/2}+C