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Popular >

integral of x+tan(x)

Solution

\int x + tan (x) d x

Solution

\frac{x ^{2}}{2} - ln ∣ cos (x) ∣ + C

Solution steps

\int x + tan (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 x d x + \int tan (x) d x

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

\int tan (x) d x = - ln ∣ cos (x) ∣

= \frac{x ^{2}}{2} - ln ∣ cos (x) ∣

Add a constant to the solution

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

Popular Examples

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\frac{( s )}{( s ^{2} + 6 s + 25 )}

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\frac{d}{d x} ((4 x + 6) (9 x - 5))

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\frac{x + 7}{x}

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\frac{d}{d x} ((cos (x)) (cos (x)))

Frequently Asked Questions (FAQ)

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