Mathematics OpenStudy (anonymous):

How to solve these integrals? integrate (secx)^2 tanx dx integrate xsec(x^2)tan(x^2) dx OpenStudy (anonymous):

For the first one:$$u=\tan x,\ du=\sec^2x\ dx$$. OpenStudy (anonymous):

For the second one: $$u=x^2,\ du=2x\ dx$$, so $\int x\sec(x^2)\tan(x^2)dx=\frac{1}{2}\int\sec u\tan u\ du=\frac{1}{2}\sec u.$ OpenStudy (anonymous):

for the first one using u=tanx, I get an answer of 0.5(tanx)^2+C when the actual answer is 0.5(secx)^2+C (by using u=secx) shouldn't both substitutions give the same answer. OpenStudy (anonymous):

Those two solutions are actually equivalent. Remember, $$\tan^2x+1=\sec^2x$$, so $$\tan^2x+1+C=\sec^2x+C$$, and $$C+1=C$$. OpenStudy (anonymous):

For further proof, derive both $$\tan^2x$$ and $$\sec^2x$$. You'll get the same thing :)

Latest Questions Tyrion: Pyramid A is a square pyramid with a base side length of 7 inches and a height of 6 inches.
5 minutes ago 0 Replies 0 Medals JeliseWh05: What are the main similarities and differences between fascism and communism?
1 hour ago 1 Reply 0 Medals JeliseWh05: What are the main similarities and differences between fascism and communism?
1 hour ago 0 Replies 0 Medals emilybethch: Identify the layers of the Sun's interior based on the brief descriptions provided.
2 hours ago 1 Reply 0 Medals emilybethch: Explain the difference between physical activity and exercise.
2 hours ago 0 Replies 0 Medals abbyadams: Which expression demonstrates the use of the commutative property of addition in
2 hours ago 0 Replies 0 Medals russianmafiya: https://strawpoll.com/wv3rw9527 it is multiple choice
2 hours ago 1 Reply 0 Medals russianmafiya: https://strawpoll.com/wbcfhgf1j
2 hours ago 5 Replies 0 Medals emilybethch: what's the right answer?
2 hours ago 4 Replies 0 Medals emilybethch: Aliza needs to run at a rate faster than 8.8 feet per second in order to exceed her fastest time in a race.
2 hours ago 3 Replies 0 Medals