Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,433 questions

17,804 answers

1,438 comments

47,235 users

Find the integral of these two equations.?

+2 votes
Use u-substitution and include steps please. I have only been able to find examples which have the complicated function on the bottom rather than on top. please help!

1) (1-sin^2x)/(cosx)dx
2) (x^4+1)/(x)dx
asked Feb 19, 2013 in CALCULUS by dkinz Apprentice

1 Answer

+3 votes

1). ʃ[(1 - sin2x)/(cos(x))]dx

Pythagorean Identities: sin2θ + cos2θ = 1 ⇒ cos2θ = 1 - sin2θ

ʃ[cos2x/cos(x)]dx

ʃcos(x)dx

Integrals of trigonometric function: ʃcos(θ)dθ = sinθ + c

sin(x) + c.

 

2). ʃ[(x4 + 1)/x]dx

ʃ[x4/x + 1/x]dx

ʃ[x3 +1/x ]dx

ʃ[x3]dx + ʃ[1/x ]dx

Integrals of rational function formula: ʃxn = [xn+1]/[n+1] + c and ʃ[1/x]dx = log(x) + c.

[x4/4] + log(x) + c.

answered Feb 19, 2013 by richardson Scholar

Related questions

...