{x³+3x+4}{{x}}\,dx - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Find the following integrals in Exercises 6 to 20.

Question : 12 of 271

Marks: +1, -0

\int\frac{x^3+3x+4}{\sqrt{x}}\,dx

Solution:

Let

I=\int\frac{x^3+3x+4}{\sqrt{x}}\,dx

=\int(x^{5/2}+3x^{1/2}+4x^{-1/2})\,dx

=\frac{x^{7/2}}{\frac{7}{2}}+\frac{3x^{3/2}}{\frac{3}{2}}+\frac{4x^{1/2}}{\frac{1}{2}}+C

=\frac{2}{7}x^{7/2}+2x^{3/2}+8\sqrt{x}+C

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