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

The integral of (2x+3cos(x)) is x^2+3sin(x)+C

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

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

x^{2} + 3 sin (x) + C

Solution steps

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

\int 2 x d x = x^{2}

\int 3 cos (x) d x = 3 sin (x)

= x^{2} + 3 sin (x)

Add a constant to the solution

= x^{2} + 3 sin (x) + C

\int \frac{sec ^{6} ( θ )}{tan ^{2} ( θ )} d θ

\int a \cdot e^{- a x} d x

\int \frac{1}{( cos ^{2} ( x ) 1 + tan ( x ) )} d x

\int \frac{arctan ^{3} ( x )}{3 x ^{2} + 3} d x

\int arctan (tan (t)) d t

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