What is the integral of (x^{3/2}+8x+2) ?

The integral of (x^{3/2}+8x+2) is 2/5 x^{5/2}+4x^2+2x+C

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integral of (x^{3/2}+8x+2)

\int (x^{\frac{3}{2}} + 8 x + 2) d x

\frac{2}{5} x^{\frac{5}{2}} + 4 x^{2} + 2 x + C

Solution steps

\int x^{\frac{3}{2}} + 8 x + 2 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 x^{\frac{3}{2}} d x + \int 8 x d x + \int 2 d x

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

\int 8 x d x = 4 x^{2}

\int 2 d x = 2 x

= \frac{2}{5} x^{\frac{5}{2}} + 4 x^{2} + 2 x

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} + 4 x^{2} + 2 x + C

\frac{d}{d x} (2 arctan (3 x) - ln (2 + 3 x))

\int_{3}^{6} \frac{1}{36 - x ^{2}} d x

f (t) = ln (cos (t))

f (x) = e^{x} cos (x), (0, 1)

\frac{\partial}{\partial x} (ln (7 x^{2} + y^{2} + 6))

What is the integral of (x^{3/2}+8x+2) ?
The integral of (x^{3/2}+8x+2) is 2/5 x^{5/2}+4x^2+2x+C