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Popular >

integral of 1/((c^2+x^2))

Solution

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

Solution

\frac{1}{c} arctan (\frac{x}{c}) + C

Solution steps

\int \frac{1}{c ^{2} + x ^{2}} d x

Apply Integral Substitution

= \int \frac{1}{c ( u ^{2} + 1 )} d u

Take the constant out:

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

= \frac{1}{c} \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= \frac{1}{c} arctan (u)

Substitute back

u = \frac{x}{c}

= \frac{1}{c} arctan (\frac{x}{c})

Add a constant to the solution

= \frac{1}{c} arctan (\frac{x}{c}) + C

Popular Examples

\frac{d}{d t} (2 e^{t})

integral of (11x^2)/((64+x^2)^2)

\int \frac{11 x ^{2}}{( 64 + x ^{2} ) ^{2}} d x

(\partial)/(\partial y)(-e^{-y/x})

\frac{\partial}{\partial y} (- e^{- \frac{y}{x}})

\frac{d y}{d x} + 8 y = 9

integral of xtan(2x)

\int x tan (2 x) d x

Frequently Asked Questions (FAQ)

What is the integral of 1/((c^2+x^2)) ?
The integral of 1/((c^2+x^2)) is 1/c arctan(x/c)+C