### Home > APCALC > Chapter 6 > Lesson 6.5.1 > Problem6-174

6-174.

Examine the integrals below. Consider the multiple tools available for evaluating integrals and use the best strategy for each part. Evaluate each integral and briefly describe your method.

1. $\int _ { 1 } ^ { 10 } 2 \sqrt { x - 1 } d x$

Convert the radical to an exponent. Then use the form $u^{power}du$.

1. $\int ( 3 x - 2 ) ^ { 2 } d x$

If $u = (3x − 2)$, then you need to add a $du$. In this case, it would be $3 dx$.
Since you already have a $dx$, add a $3$ taking out a $(1/3)$ to compensate.

Multiply $(3x − 2) (3x − 2)$.
Then take the antiderivative.

1. $\int - \frac { 1 } { 1 + x ^ { 2 } } d x$

Use the rule for one of the inverse trig functions.

1. $\int ( 6 t ^ { - 3 / 2 } + 7 t ^ { 1 / 4 } ) d t$

This is a sum of power functions. Take the antiderivative.