What is the integral of x/(sqrt(x^2-15)) ?

The integral of x/(sqrt(x^2-15)) is sqrt(x^2-15)+C

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integral of x/(sqrt(x^2-15))

integral

\frac{x}{x ^{2} - 15}

x^{2} - 15 + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

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

Substitute back

u = x^{2} - 15

= \frac{1}{2} \cdot 2 (x^{2} - 15)^{\frac{1}{2}}

Simplify

\frac{1}{2} \cdot 2 (x^{2} - 15)^{\frac{1}{2}} : x^{2} - 15

= x^{2} - 15

Add a constant to the solution

= x^{2} - 15 + C

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

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

x \cdot (x - 1)^{3}

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

\frac{x - 1}{x}

What is the integral of x/(sqrt(x^2-15)) ?
The integral of x/(sqrt(x^2-15)) is sqrt(x^2-15)+C