What is the integral of-25cos(5t+pi) ?

The integral of-25cos(5t+pi) is 5sin(5t)+C

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integral of-25cos(5t+pi)

\int - 25 cos (5 t + π) d t

5 sin (5 t) + C

Solution steps

\int - 25 cos (5 t + π) d t

Take the constant out:

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

= - 25 \cdot \int cos (5 t + π) d t

Rewrite using trig identities

= - 25 \cdot \int - cos (5 t) d t

Take the constant out:

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

= - 25 (- \int cos (5 t) d t)

Apply u-substitution

= - 25 (- \int cos (u) \frac{1}{5} d u)

Take the constant out:

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

= - 25 (- \frac{1}{5} \cdot \int cos (u) d u)

Use the common integral:

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

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

Substitute back

u = 5 t

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

Simplify

- 25 (- \frac{1}{5} sin (5 t)) : 5 sin (5 t)

= 5 sin (5 t)

Add a constant to the solution

= 5 sin (5 t) + C

\int 3 e^{2} d x

\frac{d}{d x} (\frac{x ^{2} + 4}{4 - x ^{2}})

y^{^{'}} = y - x^{2}

d er i v a t i v e arcsin (x^{3})

f (x) = 7 - x^{3}

What is the integral of-25cos(5t+pi) ?
The integral of-25cos(5t+pi) is 5sin(5t)+C