What is the integral of (3-x)/(sqrt(2x^2-12x+1)) ?

The integral of (3-x)/(sqrt(2x^2-12x+1)) is -1/2 sqrt(2x^2-12x+1)+C

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integral of (3-x)/(sqrt(2x^2-12x+1))

\int \frac{3 - x}{2 x ^{2} - 12 x + 1} d x

- \frac{1}{2} 2 x^{2} - 12 x + 1 + C

Solution steps

\int \frac{3 - x}{2 x ^{2} - 12 x + 1} d x

Apply u-substitution

= \int - \frac{u}{2 u ^{2} - 17} d u

Take the constant out:

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

= - \int \frac{u}{2 u ^{2} - 17} d u

Apply u-substitution

= - \int \frac{1}{4 v} d v

Take the constant out:

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

= - \frac{1}{4} \cdot \int \frac{1}{v} d v

Apply the Power Rule

= - \frac{1}{4} \cdot 2 v^{\frac{1}{2}}

Substitute back

= - \frac{1}{4} \cdot 2 (2 (3 - x)^{2} - 17)^{\frac{1}{2}}

Simplify

- \frac{1}{4} \cdot 2 (2 (3 - x)^{2} - 17)^{\frac{1}{2}} : - \frac{1}{2} 2 x^{2} - 12 x + 1

= - \frac{1}{2} 2 x^{2} - 12 x + 1

Add a constant to the solution

= - \frac{1}{2} 2 x^{2} - 12 x + 1 + C

What is the integral of (3-x)/(sqrt(2x^2-12x+1)) ?
The integral of (3-x)/(sqrt(2x^2-12x+1)) is -1/2 sqrt(2x^2-12x+1)+C