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Popular >

integral of 3x^{-7}

Solution

\int 3 x^{- 7} d x

Solution

- \frac{1}{2 x ^{6}} + C

Solution steps

\int 3 x^{- 7} d x

Take the constant out:

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

= 3 \cdot \int x^{- 7} d x

Apply the Power Rule

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

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

Simplify

3 (- \frac{1}{6 x ^{6}}) : - \frac{1}{2 x ^{6}}

= - \frac{1}{2 x ^{6}}

Add a constant to the solution

= - \frac{1}{2 x ^{6}} + C

Popular Examples

integral of (x-4)/(x^2+25)

\int \frac{x - 4}{x ^{2} + 25} d x

integral of xe^{18x}

\int x e^{18 x} d x

integral of ((x+3))/(x^2+2x+10)

\int \frac{( x + 3 )}{x ^{2} + 2 x + 10} d x

integral of 6/(x^3-8)

\int \frac{6}{x ^{3} - 8} d x

integral of x^2(1+x^3)^{10}

\int x^{2} (1 + x^{3})^{10} d x

Frequently Asked Questions (FAQ)

What is the integral of 3x^{-7} ?
The integral of 3x^{-7} is -1/(2x^6)+C