What is the integral from 0 to 3/2 of 1/(36+16x^2) ?

The integral from 0 to 3/2 of 1/(36+16x^2) is pi/(96)

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integral from 0 to 3/2 of 1/(36+16x^2)

\int_{0}^{\frac{3}{2}} \frac{1}{36 + 16 x ^{2}} d x

\frac{π}{96}

Decimal Notation

0.03272 \dots

Solution steps

\int_{0}^{\frac{3}{2}} \frac{1}{36 + 16 x ^{2}} d x

Apply Integral Substitution

= \int_{0}^{1} \frac{1}{24 ( 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}{24} \cdot \int_{0}^{1} \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= \frac{1}{24} [arctan (u)]_{0}^{1}

Compute the boundaries:

\frac{π}{4}

= \frac{1}{24} \cdot \frac{π}{4}

Simplify

= \frac{π}{96}

\frac{1}{( 16 x ^{2} )}, x, \frac{x}{6}

j = 0 \sum \infty \frac{7}{5 ^{j}}

\frac{d}{d x} (\frac{x}{cos ( x )})

\frac{\partial}{\partial x} (x e^{4 x + 2 y})

\int \frac{1}{6 + 2 x} d x

What is the integral from 0 to 3/2 of 1/(36+16x^2) ?
The integral from 0 to 3/2 of 1/(36+16x^2) is pi/(96)