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Popular >

integral of x^4+1/x

Solution

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

Solution

\frac{x ^{5}}{5} + ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{5}}{5} + ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{5}}{5} + ln ∣ x ∣ + C

Graph

Popular Examples

integral of 1/5 xe^{-x+1}

\int \frac{1}{5} x e^{- x + 1} d x

integral of 5-e^{-x}

\int 5 - e^{- x} d x

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

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

integral of (e^{3/t})/(t^2)

\int \frac{e ^{\frac{3}{t}}}{t ^{2}} d t

integral of cos(x)x^3

\int cos (x) x^{3} d x

Frequently Asked Questions (FAQ)

What is the integral of x^4+1/x ?
The integral of x^4+1/x is (x^5)/5+ln|x|+C