Sunday

February 1, 2015

February 1, 2015

Posted by **Zooey** on Tuesday, September 27, 2011 at 7:24pm.

Indefinite integral tan^3(pix/7)sec^2(pix/7)dx

2. Find the indefinite integral by making the substitution x=3tan(theta).

Indefinite integral x*sqrt(9+x^2)dx

3. Find the indefinite integral.

Indefinite integral cos(x)sin^3(x)dx

- Calc BC -
**Steve**, Wednesday, September 28, 2011 at 5:06amrecall that tan' = sec^2

If we let v = pi/7 x, then dv = pi/7 dx

and we have Int[tan^3(v) sec^2(v)] 7/pi dv

Now, let u = tan(v). du = sec^2(v) dv Our integral now becomes

7/pi Int[u^3 du] = 7/pi * 1/4 u^4 + C

= 7/4pi tan^4(pi/7 x) + C

----------------------

If x = 3tan(u) then 9+x^2 = 9 + 9tan^2(u) = 9 sec^2(u)

dx = 3sec^2(u) du

The integral now becomes

Int[3tan(u) * 3sec*u)* 3sec^2(u)] du = 9Int[sec(u) tan(u)*sec^2(u)]

Now, if v = sec(u), dv = sec(u) tan(u) du, and the integral now becomes

9 Int[v^2 dv] = 1/3 v^3 = 1/33 sec^3(u) = 1/3 sqrt(9+x^2)^(3/2) + C

------

This could also have been obtained by letting u=9+x^2, so du = 2xdx, making the integral

Int[u^1/2 * du/2] = 1/3(9+x^2)^(3/2) + C

--------------------------------

Let u = sin(x), so du = cos(x) dx and the integral becomes

Int[u^3 du] = 1/4 u^4 = 1/4 sin^4(x) + C

**Answer this Question**

**Related Questions**

Calculus - Hello Everyone, I need help with Calc II. 1. Integral from 0 to 1 of...

Math - 1. Evaluate the indefinite integral ([6x^2 + 12x^(3/2) +4x+9]/sqrt x)dx. ...

Calculus II/III - A. Find the integral of the following function. Integral of (x...

math - Evaluate the following indefinite integral by using the given ...

math - Evaluate the following indefinite integral by using the given ...

Integrals- Log/Ln - Can you check this please i'm not sure why it's wrong .__. 1...

Indefinite Integrals - find the indefinite integral of (1/x)*(e^(-2log[ 3,x])) ...

Calc - Use substitution to evaluate the indefinite integral: The integral of [ (...

Calculus - Solve these indefinite and definite integrals. [integration sign] 4j-...

Calc - Find the indefinite integral. Integral of [1/(4+3x²)]dx Thank you so much...