What is the integral of 8x^3+3sin(x) ?

The integral of 8x^3+3sin(x) is 2x^4-3cos(x)+C

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integral of 8x^3+3sin(x)

\int 8 x^{3} + 3 sin (x) d x

2 x^{4} - 3 cos (x) + C

Solution steps

\int 8 x^{3} + 3 sin (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 8 x^{3} d x + \int 3 sin (x) d x

\int 8 x^{3} d x = 2 x^{4}

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

= 2 x^{4} - 3 cos (x)

Add a constant to the solution

= 2 x^{4} - 3 cos (x) + C

\int_{2}^{3} \frac{2 x - 3}{4 x - x ^{2}} d x

\int sin (3 x - 2) e^{2 x} d x

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

y^{^{''}} + 2 y = sin (2 x)

\frac{d}{d x} (\frac{x ^{4} - 3 x ^{2} + 1}{( 2 x + 3 ) ^{4}})

What is the integral of 8x^3+3sin(x) ?
The integral of 8x^3+3sin(x) is 2x^4-3cos(x)+C