What is the integral of 3x+2cos(5x) ?

The integral of 3x+2cos(5x) is (3x^2)/2+2/5 sin(5x)+C

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integral of 3x+2cos(5x)

\int 3 x + 2 cos (5 x) d x

\frac{3 x ^{2}}{2} + \frac{2}{5} sin (5 x) + C

Solution steps

\int 3 x + 2 cos (5 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 3 x d x + \int 2 cos (5 x) d x

\int 3 x d x = \frac{3 x ^{2}}{2}

\int 2 cos (5 x) d x = \frac{2}{5} sin (5 x)

= \frac{3 x ^{2}}{2} + \frac{2}{5} sin (5 x)

Add a constant to the solution

= \frac{3 x ^{2}}{2} + \frac{2}{5} sin (5 x) + C

\int e^{0.5 t} d t

x \to 2 lim (\frac{( 3 x - 6 )}{1 - 4 x - 7})

\frac{\partial}{\partial x} (y^{3} + x^{2} y - 3 y)

\frac{\partial}{\partial y} (x^{2} y^{3})

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

What is the integral of 3x+2cos(5x) ?
The integral of 3x+2cos(5x) is (3x^2)/2+2/5 sin(5x)+C