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Popular >

integral of sin(5x-2)

Solution

\int sin (5 x - 2) d x

Solution

- \frac{1}{5} cos (5 x - 2) + C

Solution steps

\int sin (5 x - 2) d x

Apply u-substitution

: \int sin (u) \frac{1}{5} d u

= \int sin (u) \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{5} (- cos (u))

Substitute back

u = 5 x - 2

= \frac{1}{5} (- cos (5 x - 2))

Simplify

= - \frac{1}{5} cos (5 x - 2)

Add a constant to the solution

= - \frac{1}{5} cos (5 x - 2) + C

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\int (sin (x))^{4} cos (x) d x

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\int e^{x} - 6 cos (x) d x

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\int \frac{x \cdot arctan ( x )}{1 + x ^{2}} d x

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\int x cos (2 x + 1) d x

integral of 1/(x^8(1+x^2))

\int \frac{1}{x ^{8} ( 1 + x ^{2} )} d x

Frequently Asked Questions (FAQ)

What is the integral of sin(5x-2) ?
The integral of sin(5x-2) is -1/5 cos(5x-2)+C