What is the integral of (50+2x)^{3/2} ?

The integral of (50+2x)^{3/2} is (50+2x)^{3/2}x-6*2^{1/2}(1/5 (x+25)^{5/2}-25/3 (x+25)^{3/2})+C

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integral of (50+2x)^{3/2}

\int (50 + 2 x)^{\frac{3}{2}} d x

(50 + 2 x)^{\frac{3}{2}} x - 6 \cdot 2^{\frac{1}{2}} (\frac{1}{5} (x + 25)^{\frac{5}{2}} - \frac{25}{3} (x + 25)^{\frac{3}{2}}) + C

Solution steps

\int (50 + 2 x)^{\frac{3}{2}} d x

Apply Integration By Parts

: (50 + 2 x)^{\frac{3}{2}} x - \int 3 (50 + 2 x)^{\frac{1}{2}} x d x

= (50 + 2 x)^{\frac{3}{2}} x - \int 3 (50 + 2 x)^{\frac{1}{2}} x d x

\int 3 (50 + 2 x)^{\frac{1}{2}} x d x = 6 \cdot 2^{\frac{1}{2}} (\frac{1}{5} (x + 25)^{\frac{5}{2}} - \frac{25}{3} (x + 25)^{\frac{3}{2}})

= (50 + 2 x)^{\frac{3}{2}} x - 6 \cdot 2^{\frac{1}{2}} (\frac{1}{5} (x + 25)^{\frac{5}{2}} - \frac{25}{3} (x + 25)^{\frac{3}{2}})

Add a constant to the solution

= (50 + 2 x)^{\frac{3}{2}} x - 6 \cdot 2^{\frac{1}{2}} (\frac{1}{5} (x + 25)^{\frac{5}{2}} - \frac{25}{3} (x + 25)^{\frac{3}{2}}) + C

f (x) = 5 - 3 (1 + x^{2})^{- 1}

x \to 1 lim (\frac{2 x ^{3} - 14 x ^{2} + 12 x}{x ^{3} - 10 x ^{2} + 27 x - 18})

x \cdot \frac{d y}{d x} + y = y^{2} x^{2} ln (x)

cos (a^{6} + x^{6})

\frac{d}{d x} (ln (b - a x))

What is the integral of (50+2x)^{3/2} ?
The integral of (50+2x)^{3/2} is (50+2x)^{3/2}x-6*2^{1/2}(1/5 (x+25)^{5/2}-25/3 (x+25)^{3/2})+C