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

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

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integral of cos(x+pi/2)

\int cos (x + \frac{π}{2}) d x

cos (x) + C

Solution steps

\int cos (x + \frac{π}{2}) d x

Rewrite using trig identities

= \int - sin (x) d x

Take the constant out:

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

= - \int sin (x) d x

Use the common integral:

\int sin (x) d x = - cos (x)

= - (- cos (x))

Simplify

= cos (x)

Add a constant to the solution

= cos (x) + C

x \to π + lim (h (x))

\frac{d}{d x} ((7 x^{6} + 8 x^{3})^{4})

y^{^{'}} = x - y

(2.9) (5.8)

\int \frac{1}{1 + 4 x} d x