What is the integral of xsec^2(x^2+7) ?

The integral of xsec^2(x^2+7) is 1/2 tan(x^2+7)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xsec^2(x^2+7)

\int x sec^{2} (x^{2} + 7) d x

\frac{1}{2} tan (x^{2} + 7) + C

Solution steps

\int x sec^{2} (x^{2} + 7) d x

Apply u-substitution

: \int \frac{sec ^{2} ( u )}{2} d u

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

Take the constant out:

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

= \frac{1}{2} \cdot \int sec^{2} (u) d u

Use the common integral:

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

= \frac{1}{2} tan (u)

Substitute back

u = x^{2} + 7

= \frac{1}{2} tan (x^{2} + 7)

Add a constant to the solution

= \frac{1}{2} tan (x^{2} + 7) + C

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

\int x^{2 y} d x

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

\int x e^{- λ x} d x

\int cos (x) - \frac{3}{x ^{5}} d x

What is the integral of xsec^2(x^2+7) ?
The integral of xsec^2(x^2+7) is 1/2 tan(x^2+7)+C