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Popular >

integral of 9x^2-x^4

Solution

\int 9 x^{2} - x^{4} d x

Solution

3 x^{3} - \frac{x ^{5}}{5} + C

Solution steps

\int 9 x^{2} - x^{4} 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 9 x^{2} d x - \int x^{4} d x

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

\int x^{4} d x = \frac{x ^{5}}{5}

= 3 x^{3} - \frac{x ^{5}}{5}

Add a constant to the solution

= 3 x^{3} - \frac{x ^{5}}{5} + C

Popular Examples

integral of x^2e^{-1/2 x^2}

\int x^{2} e^{- \frac{1}{2} x^{2}} d x

integral of 4x^{1/3}+8x^{-1/3}

\int 4 x^{\frac{1}{3}} + 8 x^{- \frac{1}{3}} d x

integral of x^3+1/x-7

\int x^{3} + \frac{1}{x} - 7 d x

integral of (2^x)/(sqrt(1+4^x))

\int \frac{2 ^{x}}{1 + 4 ^{x}} d x

integral of x^3(5^{x^4+1})

\int x^{3} (5^{x^{4} + 1}) d x

Frequently Asked Questions (FAQ)

What is the integral of 9x^2-x^4 ?
The integral of 9x^2-x^4 is 3x^3-(x^5)/5+C