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Popular >

integral of 1+sec(x)

Solution

\int 1 + sec (x) d x

Solution

x + ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int 1 + sec (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 sec (x) d x

\int 1 d x = x

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= x + ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= x + ln ∣ tan (x) + sec (x) ∣ + C

Popular Examples

integral of (x-y^3+y^2sin(x))

\int (x - y^{3} + y^{2} sin (x)) d x

integral of 1/(sqrt(-x^2+2x+15))

\int \frac{1}{- x ^{2} + 2 x + 15} d x

inverse oflaplace 6/s+(32)/(s^2+16)inverse laplace

\frac{6}{s} + \frac{32}{s ^{2} + 16}

inverse oflaplace 8/((s^2+1)^2)inverse laplace

\frac{8}{( s ^{2} + 1 ) ^{2}}

x^2(dy)/(dx)-y^2=0

x^{2} \frac{d y}{d x} - y^{2} = 0

Frequently Asked Questions (FAQ)

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