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Popular >

integral of 1/(3x^7)

Solution

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

Solution

- \frac{1}{18 x ^{6}} + C

Solution steps

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

Apply the Power Rule

: - \frac{1}{6 x ^{6}}

= \frac{1}{3} (- \frac{1}{6 x ^{6}})

Simplify

\frac{1}{3} (- \frac{1}{6 x ^{6}}) : - \frac{1}{18 x ^{6}}

= - \frac{1}{18 x ^{6}}

Add a constant to the solution

= - \frac{1}{18 x ^{6}} + C

Popular Examples

integral of x^6sin(x)

\int x^{6} sin (x) d x

integral of (9x^2+5)/(3x)

\int \frac{9 x ^{2} + 5}{3 x} d x

integral of 1/((2\times 2+1)sqrt(x^2+1))

\int \frac{1}{( 2 \times 2 + 1 ) x ^{2} + 1} d x

integral of (ln(x))/(sqrt(x-1))

\int \frac{ln ( x )}{x - 1} d x

integral of (e^x)/((e^x+1)^{16)}

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{16}} d x

Frequently Asked Questions (FAQ)

What is the integral of 1/(3x^7) ?
The integral of 1/(3x^7) is -1/(18x^6)+C