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vazorg [7]
3 years ago
6

Exercise is mixed —some require integration by parts, while others can be integrated by using techniques discussed in the chapte

r on Integration.
∫x^2√x+4 dx.
Mathematics
1 answer:
wlad13 [49]3 years ago
7 0

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.  

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