What is the integral of sin(2x+3)+cos(3x-2) ?

The integral of sin(2x+3)+cos(3x-2) is -1/2 cos(2x+3)+1/3 sin(3x-2)+C

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integral of sin(2x+3)+cos(3x-2)

integral

sin (2 x + 3) + cos (3 x - 2)

- \frac{1}{2} cos (2 x + 3) + \frac{1}{3} sin (3 x - 2) + C

Solution steps

\int sin (2 x + 3) + cos (3 x - 2) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin (2 x + 3) d x + \int cos (3 x - 2) d x

\int sin (2 x + 3) d x = - \frac{1}{2} cos (2 x + 3)

\int cos (3 x - 2) d x = \frac{1}{3} sin (3 x - 2)

= - \frac{1}{2} cos (2 x + 3) + \frac{1}{3} sin (3 x - 2)

Add a constant to the solution

= - \frac{1}{2} cos (2 x + 3) + \frac{1}{3} sin (3 x - 2) + C

sin^{2} (5 x)

1 - sin^{2} (x)

1 - ∣ x ∣

(1 - x)^{3}

e^{2} x^{2}

What is the integral of sin(2x+3)+cos(3x-2) ?
The integral of sin(2x+3)+cos(3x-2) is -1/2 cos(2x+3)+1/3 sin(3x-2)+C