What is the integral of 11.5cos(0.23(t-2.7)) ?

The integral of 11.5cos(0.23(t-2.7)) is 49.99999…sin(0.23(t-2.7))+C

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integral of 11.5cos(0.23(t-2.7))

\int 11.5 cos (0.23 (t - 2.7)) d t

49.99999 \dots sin (0.23 (t - 2.7)) + C

Solution steps

\int 11.5 cos (0.23 (t - 2.7)) d t

Take the constant out:

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

= 11.5 \cdot \int cos (0.23 (t - 2.7)) d t

Apply u-substitution

: \int cos (u) \frac{1}{0.23} d u

= 11.5 \cdot \int cos (u) \frac{1}{0.23} d u

Take the constant out:

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

= 11.5 \cdot \frac{1}{0.23} \cdot \int cos (u) d u

Simplify

= 11.5 \cdot 4.34782 \dots \cdot \int cos (u) d u

Use the common integral:

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

= 11.5 \cdot 4.34782 \dots sin (u)

Substitute back

u = 0.23 (t - 2.7)

= 11.5 \cdot 4.34782 \dots sin (0.23 (t - 2.7))

Simplify

= 49.99999 \dots sin (0.23 (t - 2.7))

Add a constant to the solution

= 49.99999 \dots sin (0.23 (t - 2.7)) + C

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What is the integral of 11.5cos(0.23(t-2.7)) ?
The integral of 11.5cos(0.23(t-2.7)) is 49.99999…sin(0.23(t-2.7))+C