What is the integral of x/((1+sin^2(x)+cos^2(x))) ?

The integral of x/((1+sin^2(x)+cos^2(x))) is (x^2)/4+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x/((1+sin^2(x)+cos^2(x)))

integral

\frac{x}{( 1 + sin ^{2} ( x ) + cos ^{2} ( x ) )}

\frac{x ^{2}}{4} + C

Solution steps

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

Rewrite using trig identities

= \int \frac{x}{2} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= \frac{1}{2} \cdot \frac{x ^{2}}{2}

Simplify

\frac{1}{2} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{4}

= \frac{x ^{2}}{4}

Add a constant to the solution

= \frac{x ^{2}}{4} + C

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

\frac{( 1 + 2 x )}{( 1 - x )}

5 e^{x}

\frac{( 1 - x )}{( x ^{2} - x + 4 )}

\frac{1}{v ( v + 1 )}

What is the integral of x/((1+sin^2(x)+cos^2(x))) ?
The integral of x/((1+sin^2(x)+cos^2(x))) is (x^2)/4+C