What is the integral of sin(2x+pi/2) ?

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

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integral of sin(2x+pi/2)

\int sin (2 x + \frac{π}{2}) d x

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

Solution steps

\int sin (2 x + \frac{π}{2}) d x

Rewrite using trig identities

= \int cos (2 x) 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

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

Add a constant to the solution

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

f (x) = 3 t - t^{2}

\frac{d}{d x} (\frac{- 6}{( 1 + x ) ^{4}})

f (x) = (x^{2} + 1)^{x + 1}, at x = 0

\frac{d}{d x} (cos (\frac{1 - e ^{9 x}}{1 + e ^{9 x}}))

\int 2 x + 5 x^{- 2} d x

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