Calculus 1

Find the following indefinite integral

$\displaystyle\int 3x^6 + 5 + 7\sqrt{x}\ dx$

Find the antiderivative of $x^3$

Evaluate the following integral

$\displaystyle\int (3x + 5x^2) \ dx$

Let $f^\prime(x) = 2x$ what is the antiderivative, $f(x)$ ?

Evaluate the indefinite integral below

$\displaystyle\int (x^3 + 2x - 1) \ dx$

Evaluate the following indefinite integral

$\displaystyle\int (\sqrt{x} - 5 \sqrt[3]{x^2}) \ dx$

Evaluate the indefinite integral

$\displaystyle\int (\frac{3}{x^2} - \frac{1}{x}) \ dx$

Evaluate the indefinite integral

$\int \frac{2x^5}{x^6 + 3}^2\ dx$

Evaluate the indefinite integral

$\displaystyle\int (x^4 - \frac{1}{3\sqrt{x}} + \frac{2}{5}x^{-\frac{4}{3}}) \ dx$

Use U-Substitution to evaluate the following integral

$\displaystyle\int 4x(x^2 + 5)^{50} \ dx$

Evaluate the following integral

$\displaystyle\int\cos^4(x)\sin(x) \ dx$

Evaluate the following integral

$\displaystyle\int (x + 1) \sqrt{2x + x^2} \ dx$

Evaluate the following integral

$\displaystyle\int\frac{\sin (\ln (x))}{x} \ dx$

Evaluate the following integral

$\displaystyle\int x^3 \sin (x^4 + 2) \ dx$

Find $\displaystyle\int\sin(x)\sin(\cos{x}) \ dx$

Evaluate $\displaystyle\int x^5 \sqrt{1 + x^2} \ dx$

$\int{\frac{8}{9+r^2}}dr$

Evaluate the indefinite integral

$\displaystyle\int (x^4 + 2)^4 4x^3 \ dx$

Find $\displaystyle\int\frac{2x}{1 + 2x^2} \ dx$

Evaluate $\displaystyle\int (\ln{x})^4 \frac{2}{x} \ dx$