What is the integral of 1/((x^2+0.75)) ?

The integral of 1/((x^2+0.75)) is 1.15470…arctan(1.15470…x)+C

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integral of 1/((x^2+0.75))

integral

\frac{1}{( x ^{2} + 0.75 )}

1.15470 \dots arctan (1.15470 \dots x) + C

Solution steps

\int \frac{1}{x ^{2} + 0.75} d x

x^{2} + 0.75 = 0.75 (\frac{x ^{2}}{0.75} + 1)

= \int \frac{1}{0.75 ( \frac{x ^{2}}{0.75} + 1 )} d x

Take the constant out:

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

= \frac{1}{0.75} \cdot \int \frac{1}{\frac{x ^{2}}{0.75} + 1} d x

Simplify

= 1.33333 \dots \cdot \int \frac{1}{\frac{x ^{2}}{0.75} + 1} d x

Apply Integral Substitution

= 1.33333 \dots \cdot \int \frac{0.86602 \dots}{u ^{2} + 1} d u

Take the constant out:

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

= 1.33333 \dots \cdot 0.86602 \dots \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= 1.33333 \dots \cdot 0.86602 \dots arctan (u)

Substitute back

u = 1.15470 \dots x

= 1.33333 \dots \cdot 0.86602 \dots arctan (1.15470 \dots x)

Simplify

= 1.15470 \dots arctan (1.15470 \dots x)

Add a constant to the solution

= 1.15470 \dots arctan (1.15470 \dots x) + C

f (x) = (1 + cos (6 x))^{\frac{1}{2}}

2 (sin (x))^{3} + sin (x) + tan^{5} (x)

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

\frac{y ^{2}}{4 - 1}

(1 - n) cos (x)

What is the integral of 1/((x^2+0.75)) ?
The integral of 1/((x^2+0.75)) is 1.15470…arctan(1.15470…x)+C