7. Antiderivatives & Indefinite Integrals

Evaluate the indefinite integral as a power series: $\int \frac{1}{1-t^9} dt$.

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

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

Evaluate the definite integral if it exists: ${\int }_1^3{x}^2+2x+4 dx$

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

Find the following indefinite integral.

$\(\int\)-300dx$

Find the following indefinite integral.

$\(\int\)4x^3dx$

Find the following indefinite integral.

$\int 100x^{99}dx$

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

$h\left(x\right)=\int x^{8}dx$

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.

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

23–68. Indefinite integrals Determine the following indefinite integrals. Check your work by differentiation.

∫ (3x⁵ - 5x⁹) dx

23–68. Indefinite integrals Determine the following indefinite integrals. Check your work by differentiation.

∫ (4√x - (4 /√x)) dx

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫ (9𝓍⁸―7𝓍⁶) d𝓍