What is the integral of 1/(sqrt(7x+6)) ?

The integral of 1/(sqrt(7x+6)) is 2/7 sqrt(7x+6)+C

Popular >

integral of 1/(sqrt(7x+6))

\int \frac{1}{7 x + 6} d x

\frac{2}{7} 7 x + 6 + C

Solution steps

\int \frac{1}{7 x + 6} 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 = 7 x + 6

= \frac{1}{7} \cdot 2 (7 x + 6)^{\frac{1}{2}}

Simplify

\frac{1}{7} \cdot 2 (7 x + 6)^{\frac{1}{2}} : \frac{2}{7} 7 x + 6

= \frac{2}{7} 7 x + 6

Add a constant to the solution

= \frac{2}{7} 7 x + 6 + C

(2, 4), (5, 13)

\int (\frac{1}{3})^{x} d x

x \to 4 lim (\frac{x}{x + 1})

f (x) = 1 - e^{- \frac{x}{3}}, 2, 3

\int \frac{x ^{2} + x + 1}{x} d x

What is the integral of 1/(sqrt(7x+6)) ?
The integral of 1/(sqrt(7x+6)) is 2/7 sqrt(7x+6)+C