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Popular >

integral of x*sqrt(x^2-2)

Solution

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

Solution

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

Solution steps

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

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = x^{2} - 2

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

Simplify

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

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

Add a constant to the solution

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

Popular Examples

integral of (x^4)/((x+1)(x+2)(x+3))

\int \frac{x ^{4}}{( x + 1 ) ( x + 2 ) ( x + 3 )} d x

integral of 1/(15-x^2)

\int \frac{1}{15 - x ^{2}} d x

integral of 6sin(2x+1)

\int 6 sin (2 x + 1) d x

integral of (21)/(xsqrt(1+2x))

\int \frac{21}{x 1 + 2 x} d x

integral of (16)/(x^2-16)

\int \frac{16}{x ^{2} - 16} d x

Frequently Asked Questions (FAQ)

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