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

The integral of 7/(sqrt(x^3)) is -(14)/(sqrt(x))+C

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

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

- \frac{14}{x} + C

Solution steps

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

Take the constant out:

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

= 7 \cdot \int \frac{1}{x ^{3}} d x

Apply exponent rule:

(a^{n})^{m} = a^{n \cdot m}

x^{3} = x^{\frac{3}{2}}

= 7 \cdot \int \frac{1}{x ^{\frac{3}{2}}} d x

Apply the Power Rule

: - \frac{2}{x}

= 7 (- \frac{2}{x})

Simplify

7 (- \frac{2}{x}) : - \frac{14}{x}

= - \frac{14}{x}

Add a constant to the solution

= - \frac{14}{x} + C

\frac{d}{d x} (\frac{2 x ln ( x ) + x ^{2} - 1}{x - 1})

\int_{1}^{e^{3}} \frac{ln ^{5} ( x ^{2} )}{x} d x

35 cos (x)

\frac{d}{d t} (\frac{1 - t ^{2}}{1 + t ^{2}})

x \to - 1 lim (\frac{x ^{2} - 2}{1 - x})

What is the integral of 7/(sqrt(x^3)) ?
The integral of 7/(sqrt(x^3)) is -(14)/(sqrt(x))+C