What is the integral of (x^4)/(1+x^{10)} ?

The integral of (x^4)/(1+x^{10)} is 1/5 arctan(x^5)+C

Popular >

integral of (x^4)/(1+x^{10)}

\int \frac{x ^{4}}{1 + x ^{10}} d x

\frac{1}{5} arctan (x^{5}) + C

Solution steps

\int \frac{x ^{4}}{1 + x ^{10}} d x

Apply u-substitution

: \int \frac{1}{5 ( 1 + u ^{2} )} d u

= \int \frac{1}{5 ( 1 + u ^{2} )} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int \frac{1}{1 + u ^{2}} d u

Use the common integral:

\int \frac{1}{1 + u ^{2}} d u = arctan (u)

= \frac{1}{5} arctan (u)

Substitute back

u = x^{5}

= \frac{1}{5} arctan (x^{5})

Add a constant to the solution

= \frac{1}{5} arctan (x^{5}) + C

\int 3 e^{2 x + e^{2 x}} d x

\frac{6}{x}

\int (2 x^{4} - 1) (5 x^{3} + 6 x) d x

f (- 3) = - 2 x^{2} + 4 x - \frac{7}{x ^{2}}

\frac{d y}{d x} = y (x y^{4} - 1)

What is the integral of (x^4)/(1+x^{10)} ?
The integral of (x^4)/(1+x^{10)} is 1/5 arctan(x^5)+C