Problem 3
Evaluate the following integrals: $$ \int \frac{x^{3} d x}{\sqrt{a^{8}-x^{8}}} $$
Problem 3
Evaluate \(\int \frac{x^{3}-6 x^{2}+11 x-6}{\sqrt{x^{2}+4 x+3}} d x\)
Problem 3
Integrate \(\frac{x^{2}}{\left(x^{2}+1\right)^{2}}\) by the substitutions (a) \(x=\tan \theta\) (b) \(\mathrm{u}=\mathrm{x}^{2}+1\), and verify the argeement of the results.
Problem 3
Evaluate the following integrals : (i) \(\int \frac{1}{x \sqrt{\left(1+x^{6}\right)}} d x\) (ii) \(\int \frac{x d x}{(p x+q)^{3 / 2}}\) (iii) \(\int \frac{x^{5}}{\sqrt{\left(1+x^{2}\right.}} d x\) (iv) \(\int \frac{d x}{x^{3} \sqrt{x^{2}+1}}\)
Problem 3
\(\int x^{3} \cos 2 x d x\)
Problem 3
Evaluate the following integrals: $$ \int \frac{x}{x^{2}-5 x+6} d x $$
Problem 3
Evaluate the following integrals : $$ \int x^{-1}\left(1+x^{1 / 3}\right)^{-3} d x $$
Problem 3
Evaluate the following integrals: (i) \(\int \frac{\mathrm{dx}}{\left(\mathrm{x}^{2}+1\right) \sqrt{\mathrm{x}}}\) (ii) \(\int \frac{\mathrm{dx}}{\left(\mathrm{x}^{2}+5 \mathrm{x}+6\right) \sqrt{\mathrm{x}+1}}\) (iii) \(\int \frac{d x}{\left(x^{2}-4\right) \sqrt{x+1}}\)
Problem 4
Evaluate the following integrals : $$ \int x^{5} \sqrt[3]{\left(1+x^{3}\right)^{2}} d x $$
Problem 4
\(\int e^{-x} \cos ^{2} x d x\)
