What is the integral of 2x^{5/2} ?

The integral of 2x^{5/2} is 4/7 x^{7/2}+C

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integral of 2x^{5/2}

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

\frac{4}{7} x^{\frac{7}{2}} + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

: \frac{2}{7} x^{\frac{7}{2}}

= 2 \cdot \frac{2}{7} x^{\frac{7}{2}}

Simplify

2 \cdot \frac{2}{7} x^{\frac{7}{2}} : \frac{4}{7} x^{\frac{7}{2}}

= \frac{4}{7} x^{\frac{7}{2}}

Add a constant to the solution

= \frac{4}{7} x^{\frac{7}{2}} + C

x \to 5 lim (f (x))

y = x^{7 x}

e^{- 2 x}, 2

\frac{d y}{d x} = \frac{x}{y}, y (0) = - 3

\int \frac{1}{2 x ^{2} - 5} d x