Question

Exercise is mixed —some require integration by parts, while others can be integrated by using techniques discussed in the chapter on Integration.
∫x^2√x+4 dx.

Answer 1

Answer:

$\frac{2x^{\frac{7}{2}}}{7}+4x+c$

Step-by-step explanation:

We are asked to find the value of the indefinite integral $\int \:x^2\sqrt{x}+4\:dx$.

Let us solve our given problem applying sum rule as:

$\int \:x^2\sqrt{x}\:dx+\int \:4\:dx$

$\int \:x^2*x^{\frac{1}{2}}\:dx+\int \:4\:dx$

$\int \:x^{\frac{4}{2}}*x^{\frac{1}{2}}\:dx+\int \:4\:dx$

$\int \:x^{\frac{5}{2}}\:dx+\int \:4\:dx$

Now, we will use power rule.

$=\frac{x^{\frac{5}{2}+1}}{\frac{5}{2}+1}}+4x+c$

$=\frac{x^{\frac{7}{2}}}{\frac{7}{2}}+4x+c$

$=\frac{2x^{\frac{7}{2}}}{7}+4x+c$

Therefore, our required integral would be $\frac{2x^{\frac{7}{2}}}{7}+4x+c$.