What is the integral of (5+sqrt(3x+1)) ?

The integral of (5+sqrt(3x+1)) is 5x+2/9 (3x+1)^{3/2}+C

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integral of (5+sqrt(3x+1))

\int (5 + 3 x + 1) d x

5 x + \frac{2}{9} (3 x + 1)^{\frac{3}{2}} + C

Solution steps

\int 5 + 3 x + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 5 d x + \int 3 x + 1 d x

\int 5 d x = 5 x

\int 3 x + 1 d x = \frac{2}{9} (3 x + 1)^{\frac{3}{2}}

= 5 x + \frac{2}{9} (3 x + 1)^{\frac{3}{2}}

Add a constant to the solution

= 5 x + \frac{2}{9} (3 x + 1)^{\frac{3}{2}} + C

3 sec (x)

y^{^{'}} + y = sin (t)

\frac{d}{d x} (3 + ln (x))

\frac{e ^{- 7 s}}{s ^{2}}

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

What is the integral of (5+sqrt(3x+1)) ?
The integral of (5+sqrt(3x+1)) is 5x+2/9 (3x+1)^{3/2}+C