Question

evaluate the following:

integral sign 3/ x(x+3) (dx)

Answer 1

Use the technique of partial fractions here.

Answer 2

somebody help me with this integration problems:
\[\int\limits_{0}^{pi/2}\sin^4 x dx\]

\[\int\limits_{1}^{e}\ln x dx\]

\[\int\limits_{1}^{3}x^3 dx\]

\[\int\limits_{}dy/(4y^2-24y+27)^3/2\]

Answer 3

1. Use the identity sin^2(x)=(1-cos(2x))/2 twice.
2. Use integration by parts.
3. Use the formula \[\int x^n dx=\frac{x^{n+1}}{n+1}\]
4. I can't understand the question.

Answer 4

which part? the 3/2 is the power

can u please show me the complete solution of them all?

Answer 5

@blockcolder please do help me ....

Answer 6

\[\begin{align}
\int \frac{3}{x(x+3)} dx&=\int \frac{1}{x}-\frac{1}{x+3}\ dx\\
&=\ln{x}+\ln(x+3)+C\\
&=\ln{\left (\frac{x}{x+3} \right )}+C
\end{align}\]

Answer 7

thank you so much your a genius

Answer 8

\[\begin{align}
\int_{0}^{\pi/2} \sin^4x dx&=\int_{0}^{\pi/2} \left [ \frac{1+\cos(2x)}{2} \right ]^2 dx\\
&=\frac{1}{4} \int_{0}^{\pi/2} 1+2\cos(2x)+\cos^2(2x) dx\\
&=\frac{1}{4} \int_{0}^{\pi/2} 1+2\cos(2x)+\frac{1}{2}(1+\cos(2x))\ dx\\
&=\frac{1}{4} \left [ x+\sin(2x)+ \frac{x}{2}+\frac{\sin(2x)}{4} \right ]|_{0}^{\pi/4}\\
&= \frac{3\pi}{16}
\end{align}\]

Answer 9

thank you so much @blockcolder

Answer 10

@blockcolder how about the others?

Answer 11

\[\int_{1}^{e} \ln{x}\ dx=(x \ln{x} -x)|_{1}^{e}=1\]

Answer 12

\[\Large \int_{1}^{3}x^3\ dx=\frac{1}{4}x^4|_1^3=20\]

Answer 13

this is right wow ...

Answer 14

@blockcolder how about the last one.

Answer 15

Click "Show steps" next to the answer. It's too long to be typed here.
http://www.wolframalpha.com/input/?i=integral+of+1%2F%284x^2-24x%2B27%29^%283%2F2%29