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

The integral of x/(sqrt(x^2-3)) is sqrt(x^2-3)+C

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integral of x/(sqrt(x^2-3))

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

x^{2} - 3 + C

Solution steps

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

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

Simplify

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

= x^{2} - 3

Add a constant to the solution

= x^{2} - 3 + C

f (k) k e^{- 3 k}

y = x^{3 s i n (x)}

\int sin (x) \cdot e^{x} d x

\int \frac{400 - x ^{2}}{x} d x

\frac{\partial}{\partial x} (ln (x) + y^{3} x)

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