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

The integral of sqrt(7x-1) is 2/21 (7x-1)^{3/2}+C

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integral of sqrt(7x-1)

\int 7 x - 1 d x

\frac{2}{21} (7 x - 1)^{\frac{3}{2}} + C

Solution steps

\int 7 x - 1 d x

Apply u-substitution

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

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

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{1}{7} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 7 x - 1

= \frac{1}{7} \cdot \frac{2}{3} (7 x - 1)^{\frac{3}{2}}

Simplify

\frac{1}{7} \cdot \frac{2}{3} (7 x - 1)^{\frac{3}{2}} : \frac{2}{21} (7 x - 1)^{\frac{3}{2}}

= \frac{2}{21} (7 x - 1)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{21} (7 x - 1)^{\frac{3}{2}} + C

x \to 0 lim (\frac{1 + cos ( x )}{x})

\int \frac{x}{( x ^{2} + 1 ) ^{(\frac{3}{2})}} d x

n = 0 \sum \infty \frac{( 3 x ) ^{n}}{n}

x \to 3 lim (9)

x y^{^{'}} = 3 (x + y)

What is the integral of sqrt(7x-1) ?
The integral of sqrt(7x-1) is 2/21 (7x-1)^{3/2}+C