What is the integral of 1/(t^2+4) ?

The integral of 1/(t^2+4) is 1/2 arctan(t/2)+C

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integral of 1/(t^2+4)

\int \frac{1}{t ^{2} + 4} d t

\frac{1}{2} arctan (\frac{t}{2}) + C

Solution steps

\int \frac{1}{t ^{2} + 4} d t

Apply Integral Substitution

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

Substitute back

u = \frac{t}{2}

= \frac{1}{2} arctan (\frac{t}{2})

Add a constant to the solution

= \frac{1}{2} arctan (\frac{t}{2}) + C

\frac{d y}{d x} = \frac{x ^{4}}{y}

x \to 2 lim (x^{2} + 2 x - 5)

\int - 2 + 18 x - 12 x^{2} d x

x \to 0 lim (10 x ln (x))

\frac{d}{d x} ((2 x - 5)^{4} (x^{2} + x + 1)^{5})

What is the integral of 1/(t^2+4) ?
The integral of 1/(t^2+4) is 1/2 arctan(t/2)+C