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

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

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integral of cos(2x-1)

\int cos (2 x - 1) d x

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

Solution steps

\int cos (2 x - 1) d x

Apply u-substitution

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

= \int cos (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 cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

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

Substitute back

u = 2 x - 1

= \frac{1}{2} sin (2 x - 1)

Add a constant to the solution

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

\int_{1}^{1.5} x^{2} ln (x) d x

f (x) = \frac{sin ( x )}{e ^{x}}

\frac{x}{2}, 3 x^{2} - 1, 0, 0.5

- 9 x + 5

\frac{s ^{2} - 4}{s + 1}

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