Question

need integration help:
Integral (1/x^2)dx
Integral (e^-x)dx
Integral (sin(t))(cos(t))dt
Integral (radical s) ds

Answer 1

OK;
int(1/x^2)=(-1/x)
int(e^-x)=-e^(-x)
int (sintcost)=(1/4)sin2t
int (radical s)=1/(x^(3/2))
do you need more explanation?

Answer 2

First integral: reverse power rule
Second Integral: U-sub
3rd: U-sub
Not sure about the 4th one.

Answer 3

rewrite the integrands into known forms
\[\int{1\over x^2}dx=\int x^{-2}dx\longrightarrow{\rm solve}\\
\int e^{-x}dx\qquad\text{substiture u=-x}\\
\int \sin(t)\cos(t)dt\qquad\text{set }u=\cos(t)\\
\int \sqrt{s}ds=\int s^{1/2}ds\longrightarrow{\rm solve}
\]

Answer 4

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