What is the integral of sec^2(θ)e^{5tan(θ)} ?

The integral of sec^2(θ)e^{5tan(θ)} is 1/5 e^{5tan(θ)}+C

Popular >

integral of sec^2(θ)e^{5tan(θ)}

\int sec^{2} (θ) e^{5 t a n (θ)} d θ

\frac{1}{5} e^{5 t a n (θ)} + C

Solution steps

\int sec^{2} (θ) e^{5 t a n (θ)} d θ

Apply u-substitution

: \int e^{5 u} d u

= \int e^{5 u} d u

Apply u-substitution

: \int e^{v} \frac{1}{5} d v

= \int e^{v} \frac{1}{5} d v

Take the constant out:

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

= \frac{1}{5} \cdot \int e^{v} d v

Use the common integral:

\int e^{v} d v = e^{v}

= \frac{1}{5} e^{v}

Substitute back

= \frac{1}{5} e^{5 t a n (θ)}

Add a constant to the solution

= \frac{1}{5} e^{5 t a n (θ)} + C

\int \frac{sin ( x )}{cos ( x ) ( cos ( x ) - 1 )} d x

\int - csc^{2} (3 x) d x

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

\int 1 0^{3} x^{2} d x

\int \frac{x ^{4}}{x ^{4} + 5 x ^{2} + 4} d x

What is the integral of sec^2(θ)e^{5tan(θ)} ?
The integral of sec^2(θ)e^{5tan(θ)} is 1/5 e^{5tan(θ)}+C