What is the integral of (x^7)/(1+x^{16)} ?

The integral of (x^7)/(1+x^{16)} is 1/8 arctan(x^8)+C

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integral of (x^7)/(1+x^{16)}

\int \frac{x ^{7}}{1 + x ^{16}} d x

\frac{1}{8} arctan (x^{8}) + C

Solution steps

\int \frac{x ^{7}}{1 + x ^{16}} d x

Apply u-substitution

: \int \frac{1}{8 ( 1 + u ^{2} )} d u

= \int \frac{1}{8 ( 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}{8} \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}{8} arctan (u)

Substitute back

u = x^{8}

= \frac{1}{8} arctan (x^{8})

Add a constant to the solution

= \frac{1}{8} arctan (x^{8}) + C

(sin (y))^{^{'}}

y = \frac{x}{x + 4}, (1, 0.2)

y = \frac{1}{x}, y = x, y = \frac{1}{4} x

\int x \cdot arcsin (x) d x

(x^{2} + x^{3})^{4}

What is the integral of (x^7)/(1+x^{16)} ?
The integral of (x^7)/(1+x^{16)} is 1/8 arctan(x^8)+C