What is the integral of sqrt(7x+9) ?

The integral of sqrt(7x+9) is 2/21 (7x+9)^{3/2}+C

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integral of sqrt(7x+9)

\int 7 x + 9 d x

\frac{2}{21} (7 x + 9)^{\frac{3}{2}} + C

Solution steps

\int 7 x + 9 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 + 9

= \frac{1}{7} \cdot \frac{2}{3} (7 x + 9)^{\frac{3}{2}}

Simplify

\frac{1}{7} \cdot \frac{2}{3} (7 x + 9)^{\frac{3}{2}} : \frac{2}{21} (7 x + 9)^{\frac{3}{2}}

= \frac{2}{21} (7 x + 9)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{21} (7 x + 9)^{\frac{3}{2}} + C

\int_{1}^{4} x^{2} + 1 d x

e^{2 x^{3}}

\frac{d}{d x} (3 sec (x) tan (x))

\int sin^{2} (2 x) cos (2 x) d x

\frac{x ^{2}}{3 x + 7}

What is the integral of sqrt(7x+9) ?
The integral of sqrt(7x+9) is 2/21 (7x+9)^{3/2}+C