What is the integral from 0 to x^2+3 of 1/(x^2+3) ?

The integral from 0 to x^2+3 of 1/(x^2+3) is 1/(sqrt(3))arctan(1/(sqrt(3))(x^2+3))

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integral from 0 to x^2+3 of 1/(x^2+3)

\int_{0}^{x^{2} + 3} \frac{1}{x ^{2} + 3} d x

\frac{1}{3} arctan (\frac{1}{3} (x^{2} + 3))

Solution steps

\int_{0}^{x^{2} + 3} \frac{1}{x ^{2} + 3} d x

Apply Integral Substitution

= \int_{0}^{\frac{x ^{2} + 3}{3}} \frac{1}{3 ( 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}{3} \cdot \int_{0}^{\frac{x ^{2} + 3}{3}} \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= \frac{1}{3} [arctan (u)]_{0}^{\frac{x ^{2} + 3}{3}}

Compute the boundaries:

arctan (\frac{1}{3} (x^{2} + 3))

= \frac{1}{3} arctan (\frac{1}{3} (x^{2} + 3))

y = 2 x^{3} + 3 x^{2} - 12 x + 3

\frac{d}{d x} ((2 - x)^{4})

(u - u) (u + u)

y^{^{'}} + 2 y = e^{- x}

\int 2 x \cdot cos (x^{2}) d x

What is the integral from 0 to x^2+3 of 1/(x^2+3) ?
The integral from 0 to x^2+3 of 1/(x^2+3) is 1/(sqrt(3))arctan(1/(sqrt(3))(x^2+3))