What is the integral of (x^3)/(x^4cos^2(ln(x))) ?

The integral of (x^3)/(x^4cos^2(ln(x))) is tan(ln(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (x^3)/(x^4cos^2(ln(x)))

\int \frac{x ^{3}}{x ^{4} cos ^{2} ( ln ( x ) )} d x

tan (ln (x)) + C

Solution steps

\int \frac{x ^{3}}{x ^{4} cos ^{2} ( ln ( x ) )} d x

Simplify

\frac{x ^{3}}{x ^{4} cos ^{2} ( ln ( x ) )} : \frac{1}{x cos ^{2} ( ln ( x ) )}

= \int \frac{1}{x cos ^{2} ( ln ( x ) )} d x

Apply u-substitution

= \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= tan (u)

Substitute back

u = ln (x)

= tan (ln (x))

Add a constant to the solution

= tan (ln (x)) + C

What is the integral of (x^3)/(x^4cos^2(ln(x))) ?
The integral of (x^3)/(x^4cos^2(ln(x))) is tan(ln(x))+C