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Popular >

integral of x/(x+60)

Solution

\int \frac{x}{x + 60} d x

Solution

x + 60 - 60 ln ∣ x + 60 ∣ + C

Solution steps

\int \frac{x}{x + 60} d x

Apply u-substitution

: \int \frac{u - 60}{u} d u

= \int \frac{u - 60}{u} d u

Expand

\frac{u - 60}{u} : 1 - \frac{60}{u}

= \int 1 - \frac{60}{u} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d u - \int \frac{60}{u} d u

\int 1 d u = u

\int \frac{60}{u} d u = 60 ln ∣ u ∣

= u - 60 ln ∣ u ∣

Substitute back

u = x + 60

= x + 60 - 60 ln ∣ x + 60 ∣

Add a constant to the solution

= x + 60 - 60 ln ∣ x + 60 ∣ + C

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tangent of f(x)=-3x^2+2,\at x=1 tangent of

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f(x)=(4x^3)/(5-2x)

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Frequently Asked Questions (FAQ)

What is the integral of x/(x+60) ?
The integral of x/(x+60) is x+60-60ln|x+60|+C