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Popular >

integral of (3x^8+1)/(x^9+3x)

Solution

\int \frac{3 x ^{8} + 1}{x ^{9} + 3 x} d x

Solution

\frac{1}{3} ln x^{9} + 3 x + C

Solution steps

\int \frac{3 x ^{8} + 1}{x ^{9} + 3 x} d x

Apply u-substitution

: \int \frac{1}{3 u} d u

= \int \frac{1}{3 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} ln ∣ u ∣

Substitute back

u = x^{9} + 3 x

= \frac{1}{3} ln x^{9} + 3 x

Add a constant to the solution

= \frac{1}{3} ln x^{9} + 3 x + C

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\int x^{- 3} e^{x} d x

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\int arccsc (n t) d t

integral of ((4-x))/(sqrt(2-x^2))

\int \frac{( 4 - x )}{2 - x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of (3x^8+1)/(x^9+3x) ?
The integral of (3x^8+1)/(x^9+3x) is 1/3 ln|x^9+3x|+C