What is the integral of 3xsqrt(x^2-1) ?

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

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integral of 3xsqrt(x^2-1)

\int 3 x x^{2} - 1 d x

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

Solution steps

\int 3 x x^{2} - 1 d x

Take the constant out:

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

= 3 \cdot \int x x^{2} - 1 d x

Apply u-substitution

: \int u^{2} d u

= 3 \cdot \int u^{2} d u

Apply the Power Rule

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

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

Substitute back

u = x^{2} - 1

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

Simplify

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

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

Add a constant to the solution

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

\frac{d P}{d t} = P (0.1 - 1 0^{- 7} P)

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

z \to 2 i lim (z^{2})

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

\frac{d}{d x} (- x^{- 1})

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