List of practice Questions

Integrate the function: \(\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}\)

Integrate the function: \(\frac{1}{\sqrt{sin^{3}xsin(x+α)}}\)

Integrate the function: \(ƒ'(ax+b)[ƒ(ax+b)]^n\)

Integrate the function: \(e^{3log\ x}(x^4+1)^{-1}\)

Integrate the function: \(cos^3 x\ e^{log\ sin\ x}\)

Integrate the function: \(\frac {1}{(x^2+1)(x^2+4)}\)

Integrate the function: \(\frac {e^x}{(1+e^x)(2+e^x)}\)

Integrate the function: \(\frac {x^3}{\sqrt {1-x^8}}\)

Integrate the function: \(\frac {1}{cos(x+a)cos(x+b)}\)

Integrate the function: \(\frac{cos\,x}{\sqrt{4-sin^2x}}\)

Integrate the function: \(\frac{e^{5log\,x-e^{4\,logx}}}{e^{3\,logx}-e^{2\,logx}}\)

Integrate the function: \(\frac{sin\,x}{sin(x-a)}\)

Integrate the function: \(\frac{5x}{(x+1)(x^2+9)}\)

Integrate the function: \(\frac{1}{x^{\frac{1}{2}}+x^{\frac{1}{3}}}\) [Hint:\(\frac{1}{x^{\frac{1}{2}}+x^{\frac{1}{3}}}\)=\(\frac{1}{x^{\frac{1}{3}(1+x^{\frac{1}{6}})}}\)Put x=t⁶]

Integrate the function: \(\frac{1}{x^2(x^4+1)^{\frac{3}{4}}}\)

Integrate the function: \(\frac{1}{x\sqrt{ax-x^2}}\)

Integrate the function: \(\frac{1}{\sqrt{x+a}+\sqrt{x+b}}\)

Integrate the function: \(\frac{1}{x-x^3}\)

By using the properties of definite integrals, evaluate the integral: \(\int_{o}^{a} \frac{\sqrt{x}}{\sqrt x+\sqrt{a-x} }dx\)

By using the properties of definite integrals, evaluate the integral: \(∫^\frac{π}{2}_0\frac{sinx-cosx}{1+sinx\,cosx\,}dx\)

By using the properties of definite integrals, evaluate the integral: \(∫^{2π}_0 cos^5 xdx\)

The value of e integral \(∫^1_\frac{1}{3}\frac{(x-x^3)}{x^4}^\frac{1}{3} dx\)  is.

By using the properties of definite integrals, evaluate the integral: \(∫_0^π\frac{xdx}{1+sinx}\)

By using the properties of definite integrals, evaluate the integral: \(∫^\frac{π}{2}_\frac{-π}{2}sin^2xdx\)

By using the properties of definite integrals, evaluate the integral: \(∫^\frac{π}{2}_0(2logsinx-logsin2x)dx\)