What is the integral of x/(sqrt(x^2-100)) ?

The integral of x/(sqrt(x^2-100)) is sqrt(x^2-100)+C

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integral of x/(sqrt(x^2-100))

\int \frac{x}{x ^{2} - 100} d x

x^{2} - 100 + C

Solution steps

\int \frac{x}{x ^{2} - 100} 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} - 100

= \frac{1}{2} \cdot 2 (x^{2} - 100)^{\frac{1}{2}}

Simplify

\frac{1}{2} \cdot 2 (x^{2} - 100)^{\frac{1}{2}} : x^{2} - 100

= x^{2} - 100

Add a constant to the solution

= x^{2} - 100 + C

\frac{d}{d x} (A \cdot e^{- 2 x} \cdot x)

\int (x^{\frac{3}{2}} + 8 x + 2) d x

\frac{d}{d x} (2 arctan (3 x) - ln (2 + 3 x))

\int_{3}^{6} \frac{1}{36 - x ^{2}} d x

f (t) = ln (cos (t))

What is the integral of x/(sqrt(x^2-100)) ?
The integral of x/(sqrt(x^2-100)) is sqrt(x^2-100)+C