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Popular >

integral of tan(x)-x

Solution

\int tan (x) - x d x

Solution

- ln ∣ cos (x) ∣ - \frac{x ^{2}}{2} + C

Solution steps

\int tan (x) - x d x

Apply the Sum Rule:

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

= \int tan (x) d x - \int x d x

\int tan (x) d x = - ln ∣ cos (x) ∣

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

= - ln ∣ cos (x) ∣ - \frac{x ^{2}}{2}

Add a constant to the solution

= - ln ∣ cos (x) ∣ - \frac{x ^{2}}{2} + C

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Frequently Asked Questions (FAQ)

What is the integral of tan(x)-x ?
The integral of tan(x)-x is -ln|cos(x)|-(x^2)/2+C