What is the integral of (1-sin(x)+tan(x)) ?

The integral of (1-sin(x)+tan(x)) is x+cos(x)-ln|cos(x)|+C

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integral of (1-sin(x)+tan(x))

\int (1 - sin (x) + tan (x)) d x

x + cos (x) - ln ∣ cos (x) ∣ + C

Solution steps

\int 1 - sin (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 1 d x - \int sin (x) d x + \int tan (x) d x

\int 1 d x = x

\int sin (x) d x = - cos (x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= x - (- cos (x)) - ln ∣ cos (x) ∣

Simplify

= x + cos (x) - ln ∣ cos (x) ∣

Add a constant to the solution

= x + cos (x) - ln ∣ cos (x) ∣ + C

\int \frac{12}{1 - x ^{2}} d x

y = 4 e^{5 x}

f (x) = x^{4} + 2 e^{x}

6

11, \frac{x ^{2}}{44}, 0, 22

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