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

The integral of 1/(cos^2(2x-1)) is 1/2 tan(-1+2x)+C

Popular >

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

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

\frac{1}{2} tan (- 1 + 2 x) + C

Solution steps

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

Rewrite using trig identities

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

Apply u-substitution

: \int sec^{2} (u) \frac{1}{2} d u

= \int sec^{2} (u) \frac{1}{2} d u

Take the constant out:

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

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

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= \frac{1}{2} tan (u)

Substitute back

u = - 1 + 2 x

= \frac{1}{2} tan (- 1 + 2 x)

Add a constant to the solution

= \frac{1}{2} tan (- 1 + 2 x) + C

\int x ln (x^{4} - 1) d x

\int t 3 2 t + 7 d t

\int sin (x) x^{3} d x

\int (sin^{5} (5 x) + cos^{3} (5 x)) d x

\int (\frac{7}{5})^{x} d x

What is the integral of 1/(cos^2(2x-1)) ?
The integral of 1/(cos^2(2x-1)) is 1/2 tan(-1+2x)+C