Question

just to see if i recall it right .....

Answer 1

\[\int sin^n(t)dt=-\frac{sin^{n-1}(t)cos(t)}{n}+\frac{(n-1)}{n}\int sin^{n-2}(t)dt\]
\[\int cos^n(t)dt=\frac{cos^{n-1}(t)sin(t)}{n}+\frac{(n-1)}{n}\int cos^{n-2}(t)dt\]
\[\int tan^n(t)dt=\frac{tan^{n-1}(t)}{n-1}-\int tan^{n-2}(t)dt\]

Answer 2

i did {S} tan(x)sec^2(x) dx using the reduction rule for tan.

then the last problem was the same thing and i did it using a usub

Answer 3

\[\int tan(t)sec^2(t)dt=\int tan(t)(tan^2(t)+1)dt\]
\[=>\int tan^3(t)+tan(t)dt\]
\[=>\frac{1}{2}tan^2(t)-\int tan(t)dt+\int tan(t)dt\]
\[=>\frac{1}{2}tan^2(t)+C\]