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Popular Calculus >

integral of 4/(5x^3)

Solution

\int \frac{4}{5 x ^{3}} d x

Solution

- \frac{2}{5 x ^{2}} + C

Solution steps

\int \frac{4}{5 x ^{3}} d x

Take the constant out:

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

= \frac{4}{5} \cdot \int \frac{1}{x ^{3}} d x

Apply the Power Rule

= \frac{4}{5} (- \frac{1}{2 x ^{2}})

Simplify

\frac{4}{5} (- \frac{1}{2 x ^{2}}) : - \frac{2}{5 x ^{2}}

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

Add a constant to the solution

= - \frac{2}{5 x ^{2}} + C

Graph

Popular Examples

integral of x^4+x^3

\int x^{4} + x^{3} d x

integral of e^{tan(15x)}sec^2(15x)

\int e^{t a n (15 x)} sec^{2} (15 x) d x

integral of (3x^2)/(b^{5x^3)}

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

integral of (2x+3)/(sqrt(x^2+3x))

\int \frac{2 x + 3}{x ^{2} + 3 x} d x

integral of (1-3x)^5

\int (1 - 3 x)^{5} d x

Frequently Asked Questions (FAQ)

What is the integral of 4/(5x^3) ?
The integral of 4/(5x^3) is -2/(5x^2)+C