What is the integral of (3t+5)cos(t/4) ?

The integral of (3t+5)cos(t/4) is 4sin(t/4)(3t+5)+48cos(t/4)+C

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integral of (3t+5)cos(t/4)

\int (3 t + 5) cos (\frac{t}{4}) d t

4 sin (\frac{t}{4}) (3 t + 5) + 48 cos (\frac{t}{4}) + C

Solution steps

\int (3 t + 5) cos (\frac{t}{4}) d t

Apply Integration By Parts

: 4 sin (\frac{t}{4}) (3 t + 5) - \int 12 sin (\frac{t}{4}) d t

= 4 sin (\frac{t}{4}) (3 t + 5) - \int 12 sin (\frac{t}{4}) d t

\int 12 sin (\frac{t}{4}) d t = - 48 cos (\frac{t}{4})

= 4 sin (\frac{t}{4}) (3 t + 5) - (- 48 cos (\frac{t}{4}))

Simplify

= 4 sin (\frac{t}{4}) (3 t + 5) + 48 cos (\frac{t}{4})

Add a constant to the solution

= 4 sin (\frac{t}{4}) (3 t + 5) + 48 cos (\frac{t}{4}) + C

f (x) = 3 x^{(2)} - 5 x - 6

\frac{d}{d x} (16 x)

\frac{d}{d y} (y ln (y) - e^{- x y})

\int \frac{2 sin ( \frac{1}{5 x} )}{5 x ^{2}} d x

y = \frac{64}{16 + x ^{2}}, y = 1

What is the integral of (3t+5)cos(t/4) ?
The integral of (3t+5)cos(t/4) is 4sin(t/4)(3t+5)+48cos(t/4)+C