What is the integral of (pisin(x)+sqrt(2)cos(x)) ?

The integral of (pisin(x)+sqrt(2)cos(x)) is -picos(x)+sqrt(2)sin(x)+C

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integral of (pisin(x)+sqrt(2)cos(x))

\int (π sin (x) + 2 cos (x)) d x

- π cos (x) + 2 sin (x) + C

Solution steps

\int π sin (x) + 2 cos (x) 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 π sin (x) d x + \int 2 cos (x) d x

\int π sin (x) d x = - π cos (x)

\int 2 cos (x) d x = 2 sin (x)

= - π cos (x) + 2 sin (x)

Add a constant to the solution

= - π cos (x) + 2 sin (x) + C

\int 3 - x \cdot x^{2} d x

\int \frac{3 x 4 x ^{2} - 6}{5} d x

\int_{1}^{\infty} \frac{y}{y ^{4} + 1} d y

e^{9 x}

f (t) = sin^{2} (t)

What is the integral of (pisin(x)+sqrt(2)cos(x)) ?
The integral of (pisin(x)+sqrt(2)cos(x)) is -picos(x)+sqrt(2)sin(x)+C