What is the integral of 4sin(x)-1+8x-5 ?

The integral of 4sin(x)-1+8x-5 is 4x^2-6x-4cos(x)+C

Popular >

integral of 4sin(x)-1+8x-5

\int 4 sin (x) - 1 + 8 x - 5 d x

4 x^{2} - 6 x - 4 cos (x) + C

Solution steps

\int 4 sin (x) - 1 + 8 x - 5 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 4 sin (x) d x - \int 1 d x + \int 8 x d x - \int 5 d x

\int 4 sin (x) d x = - 4 cos (x)

\int 1 d x = x

\int 8 x d x = 4 x^{2}

\int 5 d x = 5 x

= - 4 cos (x) - x + 4 x^{2} - 5 x

Simplify

= 4 x^{2} - 6 x - 4 cos (x)

Add a constant to the solution

= 4 x^{2} - 6 x - 4 cos (x) + C

n = 1 \sum \infty \frac{n !}{2 ^{n}}

\int 7 e^{6 x} d x

\frac{d}{d x} (e^{- 10 x} - 10 e^{- 10 x} x)

3 e^{x} cos (x)

\int \frac{3 x ^{2} + x + 3}{( x - 1 ) ^{3} ( x ^{2} + 1 )} d x

What is the integral of 4sin(x)-1+8x-5 ?
The integral of 4sin(x)-1+8x-5 is 4x^2-6x-4cos(x)+C