What is the integral of e^{sin(2θ)}cos(2θ) ?

The integral of e^{sin(2θ)}cos(2θ) is 1/2 e^{sin(2θ)}+C

Popular >

integral of e^{sin(2θ)}cos(2θ)

\int e^{s i n (2 θ)} cos (2 θ) d θ

\frac{1}{2} e^{s i n (2 θ)} + C

Solution steps

\int e^{s i n (2 θ)} cos (2 θ) d θ

Apply u-substitution

: \int e^{s i n (u)} cos (u) \frac{1}{2} d u

= \int e^{s i n (u)} cos (u) \frac{1}{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 e^{s i n (u)} cos (u) d u

Apply u-substitution

: \int e^{v} d v

= \frac{1}{2} \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{2} e^{v}

Substitute back

= \frac{1}{2} e^{s i n (2 θ)}

Add a constant to the solution

= \frac{1}{2} e^{s i n (2 θ)} + C

\int \frac{( x ^{2} - 4 ) ^{2}}{2 x} d x

\int sin (6 x) sin (4 x) d x

\int z e^{z^{2} + 1} d z

\int (4 x^{\frac{1}{3}} + 6 x^{- 7} + 10) d x

\int \frac{1}{x ^{2} 25 x ^{2} + 4} d x

What is the integral of e^{sin(2θ)}cos(2θ) ?
The integral of e^{sin(2θ)}cos(2θ) is 1/2 e^{sin(2θ)}+C