What is the integral of (7^3sqrt(x^5))/2 ?

The integral of (7^3sqrt(x^5))/2 is 49x^{7/2}+C

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integral of (7^3sqrt(x^5))/2

\int \frac{7 ^{3} x ^{5}}{2} d x

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

Solution steps

\int \frac{7 ^{3} x ^{5}}{2} d x

Take the constant out:

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

= \frac{7 ^{3}}{2} \cdot \int x^{5} d x

Simplify

= \frac{343}{2} \cdot \int x^{5} d x

x^{5} = x^{\frac{5}{2}},

assuming

x \geq 0

= \frac{343}{2} \cdot \int x^{\frac{5}{2}} d x

Apply the Power Rule

= \frac{343}{2} \cdot \frac{2}{7} x^{\frac{7}{2}}

Simplify

\frac{343}{2} \cdot \frac{2}{7} x^{\frac{7}{2}} : 49 x^{\frac{7}{2}}

= 49 x^{\frac{7}{2}}

Add a constant to the solution

= 49 x^{\frac{7}{2}} + C

What is the integral of (7^3sqrt(x^5))/2 ?
The integral of (7^3sqrt(x^5))/2 is 49x^{7/2}+C