What is the integral of 1/(sqrt(4-7x)) ?

The integral of 1/(sqrt(4-7x)) is -2/7 sqrt(4-7x)+C

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integral of 1/(sqrt(4-7x))

\int \frac{1}{4 - 7 x} d x

- \frac{2}{7} 4 - 7 x + C

Solution steps

\int \frac{1}{4 - 7 x} d x

Apply u-substitution

: \int - \frac{1}{7 u} d u

= \int - \frac{1}{7 u} d u

Take the constant out:

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

= - \frac{1}{7} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

= - \frac{1}{7} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 4 - 7 x

= - \frac{1}{7} \cdot 2 (4 - 7 x)^{\frac{1}{2}}

Simplify

- \frac{1}{7} \cdot 2 (4 - 7 x)^{\frac{1}{2}} : - \frac{2}{7} 4 - 7 x

= - \frac{2}{7} 4 - 7 x

Add a constant to the solution

= - \frac{2}{7} 4 - 7 x + C

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What is the integral of 1/(sqrt(4-7x)) ?
The integral of 1/(sqrt(4-7x)) is -2/7 sqrt(4-7x)+C