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Popular >

integral of 4x^3+x^2

Solution

\int 4 x^{3} + x^{2} d x

Solution

x^{4} + \frac{x ^{3}}{3} + C

Solution steps

\int 4 x^{3} + x^{2} 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 x^{3} d x + \int x^{2} d x

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

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

= x^{4} + \frac{x ^{3}}{3}

Add a constant to the solution

= x^{4} + \frac{x ^{3}}{3} + C

Popular Examples

integral of x^3sqrt(2x+1)

\int x^{3} 2 x + 1 d x

derivative of sin(x+cos(x)+tan(x))

\frac{d}{d x} (sin (x) + cos (x) + tan (x))

d/(dy)(ln(sqrt(xy)))

\frac{d}{d y} (ln (x y))

derivative of (450t)/((t^2+6)^3)derivative of

\frac{450 t}{( t ^{2} + 6 ) ^{3}}

tangent of y=(2x)/(x^2+1),(0,0)tangent of

y = \frac{2 x}{x ^{2} + 1}, (0, 0)

Frequently Asked Questions (FAQ)

What is the integral of 4x^3+x^2 ?
The integral of 4x^3+x^2 is x^4+(x^3)/3+C