Question

integral of 7cos^t(t) dt

Answer 1

\[\int\limits_{}^{}7 \cos t = 7 \sin t +C\]
or is this
\[\int\limits_{}^{}7 \cos^{t} t \]
?

Answer 2

sorry wrote it wrong. integral of 7cos^7(t) dt

Answer 3

use reduction formula

http://www.intmath.com/methods-integration/table-common-integrals.php
look up cos^n and plug in 7 for n

Answer 4

Another option is to expand cos^7

\[7\int\limits_{?}^{?}\cos^{7}(t) = 7\int\limits_{?}^{?}\cos^{6}(t)\cos(t) =7\int\limits_{?}^{?}(\cos^{2}(t))^{3}\cos(t)=7\int\limits_{?}^{?}(1-\sin^{2}(t))^{3}\cos(t)\]
The substitute
u = sin t
du = cos t
\[\rightarrow 7\int\limits_{?}^{?}(1-u^{2})^{3} du\]