What is the integral of 7^tsin(7^t) ?

The integral of 7^tsin(7^t) is -1/(ln(7))cos(7^t)+C

Popular >

integral of 7^tsin(7^t)

\int 7^{t} sin (7^{t}) d t

- \frac{1}{ln ( 7 )} cos (7^{t}) + C

Solution steps

\int 7^{t} sin (7^{t}) d t

Apply u-substitution

: \int \frac{sin ( u )}{ln ( 7 )} d u

= \int \frac{sin ( u )}{ln ( 7 )} d u

Take the constant out:

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

= \frac{1}{ln ( 7 )} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{ln ( 7 )} (- cos (u))

Substitute back

u = 7^{t}

= \frac{1}{ln ( 7 )} (- cos (7^{t}))

Simplify

= - \frac{1}{ln ( 7 )} cos (7^{t})

Add a constant to the solution

= - \frac{1}{ln ( 7 )} cos (7^{t}) + C

\int - \frac{x}{3} + 1 d x

\int (4 x^{2} + 9 x) d x

\int x e^{8 - x^{2}} d x

\int \frac{8}{x} - \frac{5}{x ^{2}} + \frac{6}{x ^{3}} d x

\int \frac{x ^{2} + 3}{x + 2} d x

What is the integral of 7^tsin(7^t) ?
The integral of 7^tsin(7^t) is -1/(ln(7))cos(7^t)+C