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Popular >

integral of x^3-1/x

Solution

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

Solution

\frac{x ^{4}}{4} - ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{4}}{4} - ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{4}}{4} - ln ∣ x ∣ + C

Graph

Popular Examples

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\int 9^{3 d^{2} + 1} 6 dddd

integral of 5/((1-x)^2)

\int \frac{5}{( 1 - x ) ^{2}} d x

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\int \frac{cos ( x )}{( 3 + sin ( x ) )} d x

integral of 2(1-y)

\int 2 (1 - y) d y

integral of (x^6+x+1+x^{-1}+x^{-2})

\int (x^{6} + x + 1 + x^{- 1} + x^{- 2}) d x

Frequently Asked Questions (FAQ)

What is the integral of x^3-1/x ?
The integral of x^3-1/x is (x^4)/4-ln|x|+C