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Popular >

integral of 5/(usqrt(u^2-1))

Solution

\int \frac{5}{u u ^{2} - 1} d u

Solution

5 arctan (u^{2} - 1) + C

Solution steps

\int \frac{5}{u u ^{2} - 1} d u

Take the constant out:

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

= 5 \cdot \int \frac{1}{u u ^{2} - 1} d u

Apply u-substitution

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

= 5 \cdot \int \frac{1}{v ^{2} + 1} d v

Use the common integral:

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

= 5 arctan (v)

Substitute back

v = u^{2} - 1

= 5 arctan (u^{2} - 1)

Add a constant to the solution

= 5 arctan (u^{2} - 1) + C

Popular Examples

derivative of f(t)= 9/(sqrt(t))derivative of

f (t) = \frac{9}{t}

derivative of (x-5/(x^2+1))

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

integral of sin(8x-2)

\int sin (8 x - 2) d x

f^'(x)=6x^2-8x,f(3)=27

f^{^{'}} (x) = 6 x^{2} - 8 x, f (3) = 27

limit as x approaches-9 of (-3x)/(x+9)

x \to - 9 lim (\frac{- 3 x}{x + 9})

Frequently Asked Questions (FAQ)

What is the integral of 5/(usqrt(u^2-1)) ?
The integral of 5/(usqrt(u^2-1)) is 5arctan(sqrt(u^2-1))+C