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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

Popular Examples

integral of 2x^3-8x

\int 2 x^{3} - 8 x d x

integral of 1/(4x^3-x)

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

integral of 1/(cos^2(x)sqrt(1+tan^2(x)))

\int \frac{1}{cos ^{2} ( x ) 1 + tan ^{2} ( x )} d x

integral of x^{16}

\int x^{16} d x

integral of cos(3-2x)

\int cos (3 - 2 x) 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