What is the integral of (7x^3)/(4sqrt(x^6)) ?

The integral of (7x^3)/(4sqrt(x^6)) is 7/4 x+C

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integral of (7x^3)/(4sqrt(x^6))

\int \frac{7 x ^{3}}{4 x ^{6}} d x

\frac{7}{4} x + C

Solution steps

\int \frac{7 x ^{3}}{4 x ^{6}} d x

Take the constant out:

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

= \frac{7}{4} \cdot \int \frac{x ^{3}}{x ^{6}} d x

x^{6} = x^{3},

assuming

x \geq 0

= \frac{7}{4} \cdot \int \frac{x ^{3}}{x ^{3}} d x

Simplify

= \frac{7}{4} \cdot \int 1 d x

Integral of a constant:

\int a d x = a x

= \frac{7}{4} \cdot 1 \cdot x

Simplify

= \frac{7}{4} x

Add a constant to the solution

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

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What is the integral of (7x^3)/(4sqrt(x^6)) ?
The integral of (7x^3)/(4sqrt(x^6)) is 7/4 x+C