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

The integral of (2x+7)^{3/2} is 2/5 x(2x+7)^{3/2}+7/5 (2x+7)^{3/2}+C

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integral of (2x+7)^{3/2}

\int (2 x + 7)^{\frac{3}{2}} d x

\frac{2}{5} x (2 x + 7)^{\frac{3}{2}} + \frac{7}{5} (2 x + 7)^{\frac{3}{2}} + C

Solution steps

\int (2 x + 7)^{\frac{3}{2}} d x

Apply Integration By Parts

: (2 x + 7)^{\frac{3}{2}} x - \int 3 (2 x + 7)^{\frac{1}{2}} x d x

= (2 x + 7)^{\frac{3}{2}} x - \int 3 (2 x + 7)^{\frac{1}{2}} x d x

\int 3 (2 x + 7)^{\frac{1}{2}} x d x = \frac{1}{5} (3 x - 7) (2 x + 7)^{\frac{3}{2}}

= (2 x + 7)^{\frac{3}{2}} x - \frac{1}{5} (3 x - 7) (2 x + 7)^{\frac{3}{2}}

Simplify

(2 x + 7)^{\frac{3}{2}} x - \frac{1}{5} (3 x - 7) (2 x + 7)^{\frac{3}{2}} : \frac{2}{5} x (2 x + 7)^{\frac{3}{2}} + \frac{7}{5} (2 x + 7)^{\frac{3}{2}}

= \frac{2}{5} x (2 x + 7)^{\frac{3}{2}} + \frac{7}{5} (2 x + 7)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{5} x (2 x + 7)^{\frac{3}{2}} + \frac{7}{5} (2 x + 7)^{\frac{3}{2}} + C

f (x) = \frac{x}{5} + \frac{7}{x}

\frac{d}{d x} (\frac{a x - 4 1 + x}{x ^{2} - 1})

n = 1 \sum \infty (\frac{1}{e})^{n}

\int \frac{2}{3} x d x

What is the integral of (2x+7)^{3/2} ?
The integral of (2x+7)^{3/2} is 2/5 x(2x+7)^{3/2}+7/5 (2x+7)^{3/2}+C