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Popular Calculus >

integral of 1/(3x^4)

Solution

\int \frac{1}{3 x ^{4}} d x

Solution

- \frac{1}{9 x ^{3}} + C

Solution steps

\int \frac{1}{3 x ^{4}} d x

Take the constant out:

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

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

Apply the Power Rule

= \frac{1}{3} (- \frac{1}{3 x ^{3}})

Simplify

\frac{1}{3} (- \frac{1}{3 x ^{3}}) : - \frac{1}{9 x ^{3}}

= - \frac{1}{9 x ^{3}}

Add a constant to the solution

= - \frac{1}{9 x ^{3}} + C

Graph

Popular Examples

integral from-1 to 1 of 1/2 (4-4x^2)^2

\int_{- 1}^{1} \frac{1}{2} (4 - 4 x^{2})^{2} d x

(\partial}{\partial t}(\frac{s-3r)/t)

\frac{\partial}{\partial t} (\frac{s - 3 r}{t})

y^{^{''}} - y = x

derivative of 7/(3x^4)

\frac{d}{d x} (\frac{7}{3 x ^{4}})

limit as x approaches 8 of (x-8)/x

x \to 8 lim (\frac{x - 8}{x})

Frequently Asked Questions (FAQ)

What is the integral of 1/(3x^4) ?
The integral of 1/(3x^4) is -1/(9x^3)+C