What is the integral of 6^tsin(6^t) ?

The integral of 6^tsin(6^t) is -1/(ln(6))cos(6^t)+C

Popular >

integral of 6^tsin(6^t)

\int 6^{t} sin (6^{t}) d t

- \frac{1}{ln ( 6 )} cos (6^{t}) + C

Solution steps

\int 6^{t} sin (6^{t}) d t

Apply u-substitution

: \int \frac{sin ( u )}{ln ( 6 )} d u

= \int \frac{sin ( u )}{ln ( 6 )} d u

Take the constant out:

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

= \frac{1}{ln ( 6 )} \cdot \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= \frac{1}{ln ( 6 )} (- cos (u))

Substitute back

u = 6^{t}

= \frac{1}{ln ( 6 )} (- cos (6^{t}))

Simplify

= - \frac{1}{ln ( 6 )} cos (6^{t})

Add a constant to the solution

= - \frac{1}{ln ( 6 )} cos (6^{t}) + C

\int \frac{3 x}{2 x ^{2} - 9 x - 5} d x

\int 8 - x^{2} d x

\int \frac{sin ( 2 x )}{34 + cos ^{2} ( x )} d x

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

\int \frac{( x + 3 )}{( x ^{2} + 6 x )} d x

What is the integral of 6^tsin(6^t) ?
The integral of 6^tsin(6^t) is -1/(ln(6))cos(6^t)+C