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Popular >

integral of 1/(81+64x^2)

Solution

\int \frac{1}{81 + 64 x ^{2}} d x

Solution

\frac{1}{72} arctan (\frac{8}{9} x) + C

Solution steps

\int \frac{1}{81 + 64 x ^{2}} d x

Apply Integral Substitution

= \int \frac{1}{72 ( 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}{72} \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}{72} arctan (u)

Substitute back

u = \frac{8}{9} x

= \frac{1}{72} arctan (\frac{8}{9} x)

Add a constant to the solution

= \frac{1}{72} arctan (\frac{8}{9} x) + C

Popular Examples

integral of (4x^2)/(4-9x^6)

\int \frac{4 x ^{2}}{4 - 9 x ^{6}} d x

integral of 2^{x/5}

\int 2^{\frac{x}{5}} d x

integral of 6x^3-3x

\int 6 x^{3} - 3 x d x

integral of 1/(9+5x^2)

\int \frac{1}{9 + 5 x ^{2}} d x

integral of (sqrt(x^2+4))/(x^2)

\int \frac{x ^{2} + 4}{x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of 1/(81+64x^2) ?
The integral of 1/(81+64x^2) is 1/72 arctan(8/9 x)+C