What is the integral of x^1cos(-5x) ?

The integral of x^1cos(-5x) is 1/25 (5xsin(5x)+cos(5x))+C

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integral of x^1cos(-5x)

\int x^{1} cos (- 5 x) d x

\frac{1}{25} (5 x sin (5 x) + cos (5 x)) + C

Solution steps

\int x^{1} cos (- 5 x) d x

Simplify

x^{1} cos (- 5 x) : x cos (5 x)

= \int x cos (5 x) d x

Apply u-substitution

: \int \frac{u cos ( u )}{25} d u

= \int \frac{u cos ( u )}{25} d u

Take the constant out:

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

= \frac{1}{25} \cdot \int u cos (u) d u

Apply Integration By Parts

: u sin (u) - \int sin (u) d u

= \frac{1}{25} (u sin (u) - \int sin (u) d u)

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

= \frac{1}{25} (u sin (u) - (- cos (u)))

Substitute back

u = 5 x

= \frac{1}{25} (5 x sin (5 x) - (- cos (5 x)))

Simplify

= \frac{1}{25} (5 x sin (5 x) + cos (5 x))

Add a constant to the solution

= \frac{1}{25} (5 x sin (5 x) + cos (5 x)) + C

x y^{^{'}} + (x + 1) y = x, y (ln (2)) = 1

x \to 0 lim (4 x + tan (2 x))

\int 13 tan^{3} (x) d x

\frac{d}{d x} (4 x - 2 y)

9 - 1 0^{- 10} e^{40 x}

What is the integral of x^1cos(-5x) ?
The integral of x^1cos(-5x) is 1/25 (5xsin(5x)+cos(5x))+C