What is the integral of 1/(xsqrt(100x^2-100)) ?

The integral of 1/(xsqrt(100x^2-100)) is 1/10 arctan(sqrt(x^2-1))+C

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integral of 1/(xsqrt(100x^2-100))

\int \frac{1}{x 100 x ^{2} - 100} d x

\frac{1}{10} arctan (x^{2} - 1) + C

Solution steps

\int \frac{1}{x 100 x ^{2} - 100} d x

Apply Integration By Parts

: \frac{1}{10 x ^{2} - 1} - \int - \frac{2 x ^{2} - 1}{10 x ( x ^{2} - 1 ) x ^{2} - 1} d x

= \frac{1}{10 x ^{2} - 1} - \int - \frac{2 x ^{2} - 1}{10 x ( x ^{2} - 1 ) x ^{2} - 1} d x

\int - \frac{2 x ^{2} - 1}{10 x ( x ^{2} - 1 ) x ^{2} - 1} d x = - \frac{1}{10} (- \frac{1}{x ^{2} - 1} + arctan (x^{2} - 1))

= \frac{1}{10 x ^{2} - 1} - (- \frac{1}{10} (- \frac{1}{x ^{2} - 1} + arctan (x^{2} - 1)))

Simplify

\frac{1}{10 x ^{2} - 1} - (- \frac{1}{10} (- \frac{1}{x ^{2} - 1} + arctan (x^{2} - 1))) : \frac{1}{10} arctan (x^{2} - 1)

= \frac{1}{10} arctan (x^{2} - 1)

Add a constant to the solution

= \frac{1}{10} arctan (x^{2} - 1) + C

f (x) = x^{9} e^{x}

y^{\frac{1}{2}} y^{^{'}} + y^{\frac{3}{2}} = 1

\frac{d}{d x} (e^{- x} sin (2 x))

x^{2} + 2 x + 1, 2 x + 5

f (n) = 3^{n}

What is the integral of 1/(xsqrt(100x^2-100)) ?
The integral of 1/(xsqrt(100x^2-100)) is 1/10 arctan(sqrt(x^2-1))+C