What is the integral of a^{tan(θ)}sec^2(θ) ?

The integral of a^{tan(θ)}sec^2(θ) is (a^{tan(θ)})/(ln(a))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of a^{tan(θ)}sec^2(θ)

\int a^{t a n (θ)} sec^{2} (θ) d θ

\frac{a ^{t a n (θ)}}{ln ( a )} + C

Solution steps

\int a^{t a n (θ)} sec^{2} (θ) d θ

Apply u-substitution

: \int a^{u} d u

= \int a^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{a ^{u}}{ln ( a )}

Substitute back

u = tan (θ)

= \frac{a ^{t a n (θ)}}{ln ( a )}

Add a constant to the solution

= \frac{a ^{t a n (θ)}}{ln ( a )} + C

\int 3 x sin (3 x + 1) d x

\int 3 e^{0.06 x} d x

x (6 + 5 x)

\int 8 e^{2 x + 3} d x

\int (sin^{3} (x) - 3 sin^{2} (x)) (sin^{4} (x) - 4 sin^{3} (x)) 6 cos (x) d x

What is the integral of a^{tan(θ)}sec^2(θ) ?
The integral of a^{tan(θ)}sec^2(θ) is (a^{tan(θ)})/(ln(a))+C