What is the integral from 2 to 3 of 1/(x^2-6x+10) ?

The integral from 2 to 3 of 1/(x^2-6x+10) is pi/4

Popular >

integral from 2 to 3 of 1/(x^2-6x+10)

\int_{2}^{3} \frac{1}{x ^{2} - 6 x + 10} d x

\frac{π}{4}

Decimal Notation

0.78539 \dots

Solution steps

\int_{2}^{3} \frac{1}{x ^{2} - 6 x + 10} d x

Complete the square

x^{2} - 6 x + 10 : (x - 3)^{2} + 1

= \int_{2}^{3} \frac{1}{( x - 3 ) ^{2} + 1} d x

Apply u-substitution

: \int_{- 1}^{0} \frac{1}{u ^{2} + 1} d u

= \int_{- 1}^{0} \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= [arctan (u)]_{- 1}^{0}

Compute the boundaries:

\frac{π}{4}

= \frac{π}{4}

\int_{1}^{4} \frac{x}{1 + x ^{2}} d x

\int_{- 3}^{0} (\frac{y}{3} + y + 4) d y

\int_{0}^{9 π} 3 + sin (x) d x

\int_{- π}^{π} sin (x) \cdot sin (n x) d x

\int_{- 2}^{1} x^{2} - 4 d x

What is the integral from 2 to 3 of 1/(x^2-6x+10) ?
The integral from 2 to 3 of 1/(x^2-6x+10) is pi/4