Which of the following expressions is equivalent to the indefinite integral ${\int }_{}^{}(5x^3+11x+2)dx$?

Find $h\left(x\right)$ by evaluating the following indefinite integral.

$h\left(x\right)=x^{100}dx$

Find $h\left(x\right)$ by evaluating the following indefinite integral.

$h\left(x\right)=25x^{4}dx$

Find $f\left(x\right)$ by evaluating the following indefinite integral.

$f\left(x\right)=\int\left(100x^2-35x-\frac{13}{2}\right)dx$

Find $f\left(x\right)$ by evaluating the following indefinite integral.

$f\left(x\right)=\int (8x^7+10x-20)dx$

Evaluate the indefinite integral as an infinite series: ${\int }_{}^{}\left(\cos \right(x)-1)xdx$.

Evaluate the indefinite integral: $\int cos\left(6t\right) dt$

Evaluate the indefinite integral: ${\int }_{}^{}{x}^{2}dx$

Evaluate the indefinite integral. (Use c for the constant of integration.)

$${\int }_{}^{}\frac{sin\left(t\right)}{1+cos\left(t\right)} dt$$