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

The integral of a^{tan(x)}sec^2(x) is (a^{tan(x)})/(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(x)}sec^2(x)

\int a^{t a n (x)} sec^{2} (x) d x

\frac{a ^{t a n (x)}}{ln ( a )} + C

Solution steps

\int a^{t a n (x)} sec^{2} (x) d x

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 (x)

= \frac{a ^{t a n (x)}}{ln ( a )}

Add a constant to the solution

= \frac{a ^{t a n (x)}}{ln ( a )} + C

\int csc (\frac{1}{2}) x cot (\frac{1}{2}) x d x

\int cot (z) ln (sin (z)) d z

\int \frac{32}{x ^{4} + 16} d x

\int sin^{4} (5 x) cos^{5} (5 x) d x

\int \frac{1}{( 4 x ^{2} - 4 x + 27 ) ^{\frac{3}{2}}} d x

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