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

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

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

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

\frac{π}{3 3}

Decimal Notation

0.60459 \dots

Solution steps

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

Apply Integral Substitution

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

Take the constant out:

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

= \frac{1}{3} \cdot \int_{- \frac{1}{3}}^{\frac{1}{3}} \frac{1}{1 + u ^{2}} d u

Use the common integral:

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

= \frac{1}{3} [arctan (u)]_{- \frac{1}{3}}^{\frac{1}{3}}

Compute the boundaries:

\frac{π}{3}

= \frac{1}{3} \cdot \frac{π}{3}

Simplify

= \frac{π}{3 3}

\int_{1}^{8} 1 + \frac{1}{x ^{2}} d x

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

\int_{0}^{1} \frac{1}{- ln ( x )} d x

\int_{0}^{3} x^{2} + x^{2} - 4 x d x

\int_{0}^{1} x π^{x} d x

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