What is the integral of sqrt(7x+4) ?

The integral of sqrt(7x+4) is 2/21 (7x+4)^{3/2}+C

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integral of sqrt(7x+4)

\int 7 x + 4 d x

\frac{2}{21} (7 x + 4)^{\frac{3}{2}} + C

Solution steps

\int 7 x + 4 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 + 4

= \frac{1}{7} \cdot \frac{2}{3} (7 x + 4)^{\frac{3}{2}}

Simplify

\frac{1}{7} \cdot \frac{2}{3} (7 x + 4)^{\frac{3}{2}} : \frac{2}{21} (7 x + 4)^{\frac{3}{2}}

= \frac{2}{21} (7 x + 4)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{21} (7 x + 4)^{\frac{3}{2}} + C

\frac{\partial}{\partial x} (3 x y^{6} + sin (π x) - z)

\int x (6 x^{2} - x + 7) d x

x, x^{3} - 3 x^{2} + 3 x, - 0, 1

\frac{- 5 x}{2 x - 1}

e^{b x}

What is the integral of sqrt(7x+4) ?
The integral of sqrt(7x+4) is 2/21 (7x+4)^{3/2}+C