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Popular Calculus >

integral of (ax^3-b)

Solution

\int (a x^{3} - b) d x

Solution

\frac{a x ^{4}}{4} - b x + C

Solution steps

\int a x^{3} - b 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 a x^{3} d x - \int b d x

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

\int b d x = b x

= \frac{a x ^{4}}{4} - b x

Add a constant to the solution

= \frac{a x ^{4}}{4} - b x + C

Graph

Popular Examples

integral of sin(x)+e^{-x}+3x^2

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

integral of (6x)/(3x^2+1)

\int \frac{6 x}{3 x ^{2} + 1} d x

integral of (5x+1)/(sqrt(4x^2+4x+2))

\int \frac{5 x + 1}{4 x ^{2} + 4 x + 2} d x

integral of (2x^5-7x^3+6)

\int (2 x^{5} - 7 x^{3} + 6) d x

integral of (1/(2x-1))

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

Frequently Asked Questions (FAQ)

What is the integral of (ax^3-b) ?
The integral of (ax^3-b) is (ax^4)/4-bx+C