What is f(x) equal to?

If $$f(x) = a + bx + cx^{2},$$​ then $$\int_{0}^{1} f(x)\,dx$$​ is:

​$$\int \frac{\cos x + x \sin x}{x(x + \cos x)} \, dx$$ is equal to:​​

If $$f\!\left( \frac{3x-4}{3x+4} \right) = x + 2,$$​ then $$\int f(x)\,dx$$​ is equal to::

If m, n are integers and m + n is odd then the value of $$∫_0^πsin⁡mx.cos⁡nx.dx$$​ is

The Laplace transform of $$e^{at} cos ωt$$​

The value of the integral $$\int_0^{\infty} e^{-x^2} \, dx$$ is​

The value of $$\int_C \frac{3 z+1}{z(2 z+1)} d z$$​ where C is the circle |z| = 1 is:

Considering four subintervals, the value of $$\int_0^1 \frac{1}{1+x} d x$$​ by Trapezoidal rule is:

Evaluate the given expression.

$$\int \frac{\sqrt{81-(\log x)^2}}{x} d x$$​​

What is the area of the region bounded by the curve y = $$\sqrt{32-\text{x}^2}$$​ and x-axis in the first quadrant?