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Popular >

integral of x^3+3x^2

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of (e^{x-1})/(e^{x+1)}

\int \frac{e ^{x - 1}}{e ^{x + 1}} d x

integral of 1/(8-8x)

\int \frac{1}{8 - 8 x} d x

integral of (8x)/(sqrt(5x+6))

\int \frac{8 x}{5 x + 6} d x

integral of ((sqrt(x^2-9))/x)

\int (\frac{x ^{2} - 9}{x}) d x

integral of (tan(x))^5(sec(x))^3

\int (tan (x))^{5} (sec (x))^{3} d x

Frequently Asked Questions (FAQ)

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