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Popular >

integral of sin(6x-2)

Solution

\int sin (6 x - 2) d x

Solution

- \frac{1}{6} cos (6 x - 2) + C

Solution steps

\int sin (6 x - 2) d x

Apply u-substitution

: \int sin (u) \frac{1}{6} d u

= \int sin (u) \frac{1}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{6} (- cos (u))

Substitute back

u = 6 x - 2

= \frac{1}{6} (- cos (6 x - 2))

Simplify

= - \frac{1}{6} cos (6 x - 2)

Add a constant to the solution

= - \frac{1}{6} cos (6 x - 2) + C

Popular Examples

integral of (3x-sqrt(2))^5

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

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\int tan (7 x) sec^{2} (7 x) d x

integral of 8xsqrt(2x^2-1)

\int 8 x 2 x^{2} - 1 d x

integral of (x^3)/(x^2-4x+4)

\int \frac{x ^{3}}{x ^{2} - 4 x + 4} d x

integral of (mt^4+n)^5

\int (m t^{4} + n)^{5} d t

Frequently Asked Questions (FAQ)

What is the integral of sin(6x-2) ?
The integral of sin(6x-2) is -1/6 cos(6x-2)+C