What is the integral of sqrt(7x+2) ?

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

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integral of sqrt(7x+2)

\int 7 x + 2 d x

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

Solution steps

\int 7 x + 2 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 + 2

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

Simplify

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

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

Add a constant to the solution

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

\frac{5 s e ^{- s}}{2 s ^{2} + 32}

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

9 y^{^{''}} - 12 y^{^{'}} + 4 y = e^{- 3 x}

\int \frac{e ^{x}}{e ^{x} + e ^{2 x} - 2} d x

\frac{d}{d x} (x^{2} + 8)

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