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Popular >

integral of-1/x*1/x

Solution

\int - \frac{1}{x} \cdot \frac{1}{x} d x

Solution

\frac{1}{x} + C

Solution steps

\int - \frac{1}{x} \cdot \frac{1}{x} d x

Take the constant out:

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

= - \int \frac{1}{x} \cdot \frac{1}{x} d x

Simplify

\frac{1}{x} \cdot \frac{1}{x} : \frac{1}{x ^{2}}

= - \int \frac{1}{x ^{2}} d x

Apply the Power Rule

: - \frac{1}{x}

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

Simplify

= \frac{1}{x}

Add a constant to the solution

= \frac{1}{x} + C

Popular Examples

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integral of θsec(θ)tan(θ)

\int θ sec (θ) tan (θ) d θ

((f(x)+x-6)/(4-2x))'

(\frac{f ( x ) + x - 6}{4 - 2 x})^{'}

integral of (9-x^2)

\int (9 - x^{2}) d x

derivative of 16ln(x^2-x^2)

\frac{d}{d x} (16 ln (x^{2}) - x^{2})

Frequently Asked Questions (FAQ)

What is the integral of-1/x*1/x ?
The integral of-1/x*1/x is 1/x+C