A series of integral based questions?

Question

$\intx^5\ln(x)dx$
My answer: $x^6/6(\ln(x)-1/6)+C$

$\int\sec^3(x)\tan(x)dx$
My answer: $1/3\sec^3(x)+C$

$\int(x^3)/(x^2+1)dx$
My answer: $x^2/2-2\ln|x^2+1|+C$

$\int(5x)/(x^2-3x)dx$
My answer: $5\ln|x-3|+C$

Find the area of the region bounded by $y=4-x^2$ and $y=2x+1$ .
My answer: $27/3$

Find the volume of the region bounded by $y=x^3$ , $y=0$ , and $x=3$ , revolved around the y-axis.
My answer: $(243\pi)/5$

Approximate $\int_2^4\sqrt(x-2)dx$ using the Trapezoidal rule, rounding to 4 decimal places.
My answer: $\approx1.8195$

$\int_1^\infty(\tan^-1(x))/(x^2+1)dx$
My answer: divergent ( $\infty$ ) ?

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Answer 1 · 2018-03-20T00:48:59

1 - 4 check by differentiating.

5) is incorrect

6) I get the same answer

8) converges