What is the integral of cos(7x-1) ?

The integral of cos(7x-1) is 1/7 sin(7x-1)+C

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integral of cos(7x-1)

\int cos (7 x - 1) d x

\frac{1}{7} sin (7 x - 1) + C

Solution steps

\int cos (7 x - 1) d x

Apply u-substitution

: \int cos (u) \frac{1}{7} d u

= \int cos (u) \frac{1}{7} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{7} sin (u)

Substitute back

u = 7 x - 1

= \frac{1}{7} sin (7 x - 1)

Add a constant to the solution

= \frac{1}{7} sin (7 x - 1) + C

\frac{d}{d x} ((2 x + 3) (x^{2} - 5))

\frac{\partial}{\partial x} (yz e^{x z})

y^{^{'''}} + y^{^{''}} + 8 y^{^{'}} - 10 y = 0

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

\int \frac{x ^{2}}{2 x ^{3} - 1} - 2 d x

What is the integral of cos(7x-1) ?
The integral of cos(7x-1) is 1/7 sin(7x-1)+C