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Popular >

integral of tan(x)-1

Solution

\int tan (x) - 1 d x

Solution

- ln ∣ cos (x) ∣ - x + C

Solution steps

\int tan (x) - 1 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 1 d x

\int tan (x) d x = - ln ∣ cos (x) ∣

\int 1 d x = x

= - ln ∣ cos (x) ∣ - x

Add a constant to the solution

= - ln ∣ cos (x) ∣ - x + C

Popular Examples

integral of (x+1)(x^2+3)

\int (x + 1) (x^{2} + 3) d x

integral of 4xsqrt(x+3)

\int 4 x x + 3 d x

integral of ((x^2))/(x^3+1)

\int \frac{( x ^{2} )}{x ^{3} + 1} d x

integral of arcsin(w)

\int arcsin (w) d w

integral of cos(y)+ycos(x)

\int cos (y) + y cos (x) d x

Frequently Asked Questions (FAQ)

What is the integral of tan(x)-1 ?
The integral of tan(x)-1 is -ln|cos(x)|-x+C