Answer
$\frac{sin(1+5t)}{5} +C$
Work Step by Step
Evaluate the Integral using substitution: $\int cos(1+5t)dt$
Substitution Rule: $\int f(g(x))g’(x)dx = \int f(u)du$
$u= 1+5t$
$du =5$
Since $du$ in the expression is equal to $1$ it must be multiplied by $\frac{1}{5}$
Solve the integral in terms of $u$:
$\int cos(u)(\frac15)du$
$\frac{1}{5}\int cos(u)du $
$\frac{1}{5}sin(u) +C$
$\frac{sin(u)}{5} + C$
Substitute for $u$:
$\frac{sin(1+5t)}{5} +C$
