What is the integral of (x^2-sec^2(x)) ?

The integral of (x^2-sec^2(x)) is (x^3)/3-tan(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^2-sec^2(x))

\int (x^{2} - sec^{2} (x)) d x

\frac{x ^{3}}{3} - tan (x) + C

Solution steps

\int x^{2} - sec^{2} (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{2} d x - \int sec^{2} (x) d x

\int x^{2} d x = \frac{x ^{3}}{3}

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

= \frac{x ^{3}}{3} - tan (x)

Add a constant to the solution

= \frac{x ^{3}}{3} - tan (x) + C

\int e^{x} (2 x - 1) d x

\int 2^{x} \cdot 5^{x} d x

\int (x - 1)^{3} d x

\int u^{- 5} (2 - u^{5} + u^{10}) d u

\int e^{- x^{5}} x^{4} d x

What is the integral of (x^2-sec^2(x)) ?
The integral of (x^2-sec^2(x)) is (x^3)/3-tan(x)+C