What is the integral of 1/(xsqrt(8x-1)) ?

The integral of 1/(xsqrt(8x-1)) is 2arctan(sqrt(8x-1))+C

Popular >

integral of 1/(xsqrt(8x-1))

\int \frac{1}{x 8 x - 1} d x

2 arctan (8 x - 1) + C

Solution steps

\int \frac{1}{x 8 x - 1} d x

Apply u-substitution

: \int \frac{2}{u ^{2} + 1} d u

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

Take the constant out:

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

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

Use the common integral:

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

= 2 arctan (u)

Substitute back

u = 8 x - 1

= 2 arctan (8 x - 1)

Add a constant to the solution

= 2 arctan (8 x - 1) + C

\int (cot (π x) + tan (π x))^{2} d x

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

\int \frac{2}{( x - 3 ) 4 x ^{2} - 24 x + 20} d x

\int \frac{1}{x ^{2} 1 - x} d x

\int \frac{x}{4 + 3 x} d x

What is the integral of 1/(xsqrt(8x-1)) ?
The integral of 1/(xsqrt(8x-1)) is 2arctan(sqrt(8x-1))+C