What is the integral of sqrt(7x-3) ?

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

Popular >

integral of sqrt(7x-3)

\int 7 x - 3 d x

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

Solution steps

\int 7 x - 3 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 - 3

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{x}{2} e^{\frac{- 3 x}{4}} d x

\int - \frac{2}{100 - 9 x ^{2}} d x

\int - 2 + (t^{2} + 3 t)^{\frac{6}{5}} - t^{3} d x

\int \frac{x - 3}{x ^{2} - 5 x + 6} d x

\int \frac{5 x}{x ^{3} + x ^{2}} d x

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