What is the integral of cos(4x+1) ?

The integral of cos(4x+1) is 1/4 sin(4x+1)+C

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integral of cos(4x+1)

\int cos (4 x + 1) d x

\frac{1}{4} sin (4 x + 1) + C

Solution steps

\int cos (4 x + 1) d x

Apply u-substitution

: \int cos (u) \frac{1}{4} d u

= \int cos (u) \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{4} sin (u)

Substitute back

u = 4 x + 1

= \frac{1}{4} sin (4 x + 1)

Add a constant to the solution

= \frac{1}{4} sin (4 x + 1) + C

\int tan^{3} (1) d x

\frac{d}{d x} (a \cdot b^{x})

\int t^{2} d t

\frac{\partial}{\partial x} (x^{2} - x y + 3 y^{2})

\frac{\partial}{\partial x} (2 x y + x^{2} - 1)

What is the integral of cos(4x+1) ?
The integral of cos(4x+1) is 1/4 sin(4x+1)+C