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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

derivative of y=sin(x)-cos(x)derivative of

y = sin (x) - cos (x)

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

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

y^'+3y=xe^{-2x}+e^{-3x}

y^{^{'}} + 3 y = x e^{- 2 x} + e^{- 3 x}

y^{''}=x(y^')^2

y^{^{''}} = x (y^{^{'}})^{2}

tangent of x/(1+x^2),\at x=0 tangent of

\frac{x}{1 + x ^{2}}, at x = 0

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