What is the integral of 7tan(x)sec^2(x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 7tan(x)sec^2(x)

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

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

Solution steps

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

Take the constant out:

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

= 7 \cdot \int tan (x) sec^{2} (x) d x

Apply u-substitution

: \int u d u

= 7 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= 7 \cdot \frac{u ^{2}}{2}

Substitute back

u = tan (x)

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

Simplify

7 \cdot \frac{tan ^{2} ( x )}{2} : \frac{7}{2} tan^{2} (x)

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

Add a constant to the solution

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

\int x d (sin (x)) d x

\int 2 x e^{7 x^{2}} d x

\int \frac{1}{x + x} d x

\int sin^{7} (\frac{x}{5}) cos (\frac{x}{5}) d x

\int cos (2 t + 1) d t

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