What is the integral of 5sin(5x) ?

The integral of 5sin(5x) is -cos(5x)+C

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integral of 5sin(5x)

\int 5 sin (5 x) d x

- cos (5 x) + C

Solution steps

\int 5 sin (5 x) d x

Take the constant out:

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

= 5 \cdot \int sin (5 x) d x

Apply u-substitution

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

= 5 \cdot \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

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

Use the common integral:

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

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

Substitute back

u = 5 x

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

Simplify

5 \cdot \frac{1}{5} (- cos (5 x)) : - cos (5 x)

= - cos (5 x)

Add a constant to the solution

= - cos (5 x) + C

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

f (x) = x^{2} x^{3} + 1, at x = 2

\frac{d}{d x} (x^{4} ln (9 x))

n = 1 \sum \infty 2 (\frac{1}{5})^{n - 1}