What is the integral of 1/((d^2+1)cos(x)) ?

The integral of 1/((d^2+1)cos(x)) is 1/(d^2+1)ln|tan(x)+sec(x)|+C

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integral of 1/((d^2+1)cos(x))

integral

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

\frac{1}{d ^{2} + 1} ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{d ^{2} + 1} \cdot \int \frac{1}{cos ( x )} d x

Rewrite using trig identities

= \frac{1}{d ^{2} + 1} \cdot \int sec (x) d x

Use the common integral:

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

= \frac{1}{d ^{2} + 1} ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= \frac{1}{d ^{2} + 1} ln ∣ tan (x) + sec (x) ∣ + C

sin (2 x + y)

f (x) = 55 - 4 x

\frac{2 x}{( x + 1 ) ^{2}}

\frac{( x + 8 )}{x + 7}

\frac{1}{x ^{2} + y ^{2}}

What is the integral of 1/((d^2+1)cos(x)) ?
The integral of 1/((d^2+1)cos(x)) is 1/(d^2+1)ln|tan(x)+sec(x)|+C