What is the integral of (9x^2)/2-5cos(x)+7 ?

The integral of (9x^2)/2-5cos(x)+7 is (3x^3)/2-5sin(x)+7x+C

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integral of (9x^2)/2-5cos(x)+7

\int \frac{9 x ^{2}}{2} - 5 cos (x) + 7 d x

\frac{3 x ^{3}}{2} - 5 sin (x) + 7 x + C

Solution steps

\int \frac{9 x ^{2}}{2} - 5 cos (x) + 7 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 \frac{9 x ^{2}}{2} d x - \int 5 cos (x) d x + \int 7 d x

\int \frac{9 x ^{2}}{2} d x = \frac{3 x ^{3}}{2}

\int 5 cos (x) d x = 5 sin (x)

\int 7 d x = 7 x

= \frac{3 x ^{3}}{2} - 5 sin (x) + 7 x

Add a constant to the solution

= \frac{3 x ^{3}}{2} - 5 sin (x) + 7 x + C

- \frac{1}{s ^{2}}

\int e^{- c x} d x

\frac{\partial}{\partial x} (y + \frac{1}{x + y})

\frac{d}{d x} (lo g_{3} (sec (2 x)))

x \to 0 lim (tan (x) - sec (x))

What is the integral of (9x^2)/2-5cos(x)+7 ?
The integral of (9x^2)/2-5cos(x)+7 is (3x^3)/2-5sin(x)+7x+C