What is the integral of 7x^3sqrt(x) ?

The integral of 7x^3sqrt(x) is 14/9 x^{9/2}+C

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integral of 7x^3sqrt(x)

\int 7 x^{3} x d x

\frac{14}{9} x^{\frac{9}{2}} + C

Solution steps

\int 7 x^{3} x d x

Take the constant out:

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

= 7 \cdot \int x^{3} x d x

Simplify

x^{3} x : x^{\frac{7}{2}}

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

Apply the Power Rule

: \frac{2}{9} x^{\frac{9}{2}}

= 7 \cdot \frac{2}{9} x^{\frac{9}{2}}

Simplify

7 \cdot \frac{2}{9} x^{\frac{9}{2}} : \frac{14}{9} x^{\frac{9}{2}}

= \frac{14}{9} x^{\frac{9}{2}}

Add a constant to the solution

= \frac{14}{9} x^{\frac{9}{2}} + C

n = 0 \sum \infty (5 x - 3)^{n}

y = ln (3 - 2 x), at x = - 3

\int ln (x + 3) d x

\frac{d}{d x} ((3 x - 2)^{3})

y = 9 x - x^{2}, y = 2 x

What is the integral of 7x^3sqrt(x) ?
The integral of 7x^3sqrt(x) is 14/9 x^{9/2}+C