What is the integral of 1/(x^2-2x+101) ?

The integral of 1/(x^2-2x+101) is 1/10 arctan((x-1)/(10))+C

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integral of 1/(x^2-2x+101)

\int \frac{1}{x ^{2} - 2 x + 101} d x

\frac{1}{10} arctan (\frac{x - 1}{10}) + C

Solution steps

\int \frac{1}{x ^{2} - 2 x + 101} d x

Complete the square

x^{2} - 2 x + 101 : (x - 1)^{2} + 100

= \int \frac{1}{( x - 1 ) ^{2} + 100} d x

Apply u-substitution

: \int \frac{1}{u ^{2} + 100} d u

= \int \frac{1}{u ^{2} + 100} d u

Apply Integral Substitution

= \int \frac{1}{10 ( v ^{2} + 1 )} d v

Take the constant out:

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

= \frac{1}{10} \cdot \int \frac{1}{v ^{2} + 1} d v

Use the common integral:

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

= \frac{1}{10} arctan (v)

Substitute back

= \frac{1}{10} arctan (\frac{x - 1}{10})

Add a constant to the solution

= \frac{1}{10} arctan (\frac{x - 1}{10}) + C

\int sec^{5} (4 x) d x

\frac{\partial}{\partial x} (x^{x^{2} + y^{2}})

\frac{\partial}{\partial x} (y^{6} cos (4 x) \cdot 4)

n = 1 \sum \infty \frac{9}{10 0 ^{n}}

x \to 0 lim (g (x))

What is the integral of 1/(x^2-2x+101) ?
The integral of 1/(x^2-2x+101) is 1/10 arctan((x-1)/(10))+C